Hi everyone, I'm Joe for jaspyscasewrakes.com coming at you with jaspys five box through the years of contenders Football mixer. Yeah, we're going through the years of contenders here. We got 2016 we're starting with 2011 then 2016 2018 2019 and then jump to 2021 The only years are not represented a 17 in 2020 And then I guess the years in between there and there but anyway, it's a nice little nice little blast from the past Up to the present big. Thanks to this group for making it happen. Thanks to the people who bought their spots straight up And congrats to the people who who won their spots in that filler Correct list. Yeah, and of course all 32 teams are in I'm pretty sure commons won't ship. Yeah commons won't ship But everything else will So thank you again. Let's go. Let's roll it. Let's randomize names and teams four and a six ten times one two three and A tenth and final time. So we got Raymond down to Ryan After ten and then ten times for the teams one two three four Five and a tenth and final time After ten we got the bills All the way down to the Falcons All right, so Raymond Buffalo We got the Buffalo bills Dean with the Steelers Sean with the Panthers Jonathan with the Green Bay Packers Alan with the Bengals Ryan with the Seahawks Terry with the Saints Neil with the Rams Dylan with the Colts Jesse with the Titans Matthew with the Pats David with the Cardinals Patrick with the Vikings Raymond with the Chiefs Jonathan with the Lions Eric with the Cowboys and Ravens and Jonathan K with last pop mojo Cleveland Browns For you Terry with my Raiders Chris with the Niners Sean with the Dolphins David with the Broncos Nancy with the Texans Alex with the Giants Rodney with the Chargers Jonathan with the Jets Alex with the Buccaneers Matthew with the Bears Jonah with the Commanders Jonathan with the Jags Thomas with the Eagles and Ryan with the ATL the Atlanta Falcons Let's sort this alphabetically by team and We're gonna open up the trade window for everybody, but trade member trade at your own risk if you're Remember we got 2011. So think about those guys think about these guys in 2016 2018 2019 and 2021 So just keep those in mind as you are wheeling and dealing. We're gonna pause the video when we come back We'll see if any deals get done and then we'll have the break stick around BRB All right. Welcome back folks trade window is closed A lot of trade chatter, but in the end no no deals were done Which is fine. It's all good. So that list right there is a now official print it out remains the same Thanks, everybody. So we're gonna go in chronological order We're gonna go with the oldest box first and then we'll make our way to the 2021 box right here So here's 2011 checklist right here as well Now there is a chance that there's gonna be some expired redemptions in here But the risk that we're willing to take here and this is a I believe this is a wax party break That's my reminder to do the randomizer a lot of quarterback changes I think more more than Have we seen a lot more quarterback movement? More than usual What do you think's gonna be the best The best quarterback on their new team who's gonna have the most success Russell Wilson Denver's maybe Carson Wentz Washington Matt Ryan in Indianapolis Rex has a question. Have I ever thrown my hands in the air and waved them like I didn't care Yeah, I have I have on I have been known on occasion to do such such a thing Especially when prompted Especially when prompted I'm afraid not Jeremy No, no Mac or no NT baseball Is that another homerun? Anthony Rendon with a solo homer. Come on Walker Bueller. What's going on here Cleveland and Cleveland's a Sean Watson Who knows what what Seattle's gonna do with their quarterback position Mariota is in Atlanta a lot of cards in landscape mode here We'll do left-right randomizers on that even though that's the same team and our first autograph is Is a Henry Hinozki yeah a lot a lot of a lot more packs in this one than some of the other breaks we've done but More than most but not not as much as some we've we've seen some breaks where there's quite a quite a few packs My towers and who's the last quarterback to manage the game and win a Super Bowl There's Quinn Carter maybe Who is the the Ravens quarterback? Like they had a great defense and a quarterback just kind of managed it and won the Super Bowl Speaking of the Ravens here is Tara Taylor rookie ticket autograph so sorry the brah the Quinn Carter Broncos autograph goes to David and Denver and Tara Taylor Goes to Eric and the Ravens Joe Flacco, maybe wasn't there a hassle back? I feel like no, maybe I'm thinking of somebody else Maybe it was Joe Flacco Well, I think he he may have done more than manage the game yeah paid manning in his last year Ryan saying Kind of noodle arm Peyton Manning sort of had to manage they had a great defense to a great defense I think definitely wanted for him.  All right, so that was 2011 Let's get into Let's get into some 2016 Did we have a Greg little redemption in the last mixer? Yeah, it's it's kind of interesting right Mike Mike tower saying so wait you telling me that you can You don't really need a QV to win games But if you have a great defense and a running but you have to have a great defense a running game I mean Even with quarterbacks the quarterback position being so maybe Maybe nowadays is that different nowadays? Right because you can have a great quarterback said if you don't have a you don't have a great You don't have a good defense Or a running game to kind of slow down the game if you have the lead or something like that but then again so few so few times that Game-managing quarterbacks are winning Super Bowls, right? those players tend to have like Top shelf defenses. I think you would rather take the take the excellent quarterback Still rather take the take the excellent quarterback and not have to worry too much about having a top tier defense Yeah, MPPs are usually quarterbacks Sort of a quarterback award. They I think they I mean they handle the ball the most box So now we're in 2016 And our first auto is sewer Craven's Rookie ticket autograph for Washington. That's going to go to Jonah Tried to trade couldn't trade mojo and we got we got Vikings Sam Bradford nine out of ninety nine That'll be for Minnesota. That's going to go to Patrick Advertising in 2016. We've got a Kenneth Farrow for the Chargers It's going to go to Rodney and the Bolts and a Derek Wa TJ and JJ's brother, you would think they would have they would have gone with a DJ one No, but then he's on the offensive side of the ball, too So he's just like the the black sheep of the family and we got a golden ticket Larry Fitzgerald autograph Cardinals that's going to go to David Again another expired redemption, but maybe they'll do something for you Although this is part of a promo I don't know what they're going to do for you with this, but This is part of that that promo Possibly win one of those things or do you actually receive? No, it's you're eligible to receive Anyway, well, it's expired now, but we'll send that off to you, David That is the risk of some of these older products And we're doing those left-right randomizers I missed opportunity there too, right a C watt D. There's JJ one AC DC and we've got a draft class autographs 16 out of 16 Braxton Miller nice on-card autographs and good penmanship there from Braxton Miller And that will go to Nancy in the Texans. We've got a Playoff ticket card of 173 out of 249 Jeremy Macklin That'll be for KC. That's going to go to Raymond and our last auto Sheldon rankings for the Saints that's going to be for Terry and Nollins and onwards now we go to 2018 Be nice if uh This guy has a bounce back here. It'd be nice. Where's Baker gonna end up? Where does Baker may feel and It's got to go somewhere, right? I guess there's not too many places where he could go Seattle could be an option but I think you probably like not a lot of Bears there bears Browns have a lot of leverage, right? Everyone knows They got it. They got to get rid of Baker me. I mean, I guess I can keep him It just doesn't seem likely though Would it be a Baker maple II thing to do if he just stays and Then just tries to win the job outright in camp Mike tower saying I once had a Josh Rosen and Josh Allen do a lot of one-of-one Can't remember at the time which one Rosen or Allen was out these more. I'll bet the year this came out It would probably be Rosen. I think it wasn't either hired the higher draft big and I think Josh Allen at the time was still sort of a Sort of a you know, everyone knew he had a cannon for an arm But it's still sort of a raw product and we've got a Texan to kick things off Jordan Thomas It's our first auto in this box It'll be for Nancy and the Texans Not a Raven rookie ticket autograph Jordan Lazzly Eric with Baltimore Maybe the yeah instead of trading now or they're waiting for the trade deadline some teams have injured QB. That's a possibility Maybe draft Logan suggesting Jair Alexander Speaking of Logan's Packers this one is for Jonathan Yeah, Logan saying rumors are Packers trade love in the third round for a wide receiver something like that Another redemption here that we've got Kiki Kuti rookie ticket variation RPS, which is for the Texans Nancy again expired, but You may still do something for you. We'll still send it your way You got an Andrew Luck 50 s75 MVP contenders Colts that's gonna go to Dylan Nice Randall. I will pull. I mean kind of in the middle of something right now But We'll repost that once this break is over right and playoff ticket autograph MJ Stewart 84 out of 99 That's for Alex and the Buccaneers Let's move on to 2018 See if you can find These key names here. All right next box. Good luck. Yeah, I think that I think that's pretty much done I don't think anybody outside of Maybe the state of Indianapolis state of Indiana or the city of Indianapolis would are discussing Andrew Luck Return maybe local sports talk radio might bring that up But I think I think the closest we got was like was it last summer or two summers ago? we're like a friend of Andrew Luck's wife had leaked some texts text messages about like oh Andrew is Is meeting with the Colts owner for like dinner? Well, I don't know if those are if that string of text messages Were were debunked or not or if they're maybe if they were true. I Think it was just maybe just a personal dinner not maybe like a business dinner. So I Think that was as close as we got To that And then that was it and I think it's been There's been no rumors or anything like that. No one reporting on anything like that Yeah, at this point, I think I think that's that for him Right built a house near the stadium and everyone's like ooh, and we got Jermaine at Pratt Our first autograph out of here champs to take it auto 19 out of 49 That's Alan with the Bengals You got Trayvon Mullin Jr. rookie ticket autograph For my Raiders that goes to Terry Raiders are hoping Guys I can can still evolve. They need it. They're deep. Their offense is gonna be fine. They got to Take care of that defense Trayvon Williams 86 out of 99 Alan with the Bengals another redemption and Benny Snell jr rookie ticket autograph. I have no when it sells out slab That's when the mixer Will happen remember there are probably I think there are two fillers still attached to it So we got to knock those out too and when that happens, it'll be on the schedule, which you can always see pin in the chat Click that link. It'll take it to the schedule. It's Kenya Andre to 175 Dolphins addition currently a raider Injury last season kind of kind of interrupted this season by thinking still be pretty effective for the Raiders the Redemption is Devin Bush the second For the Steelers that's gonna be for Dean about that's Benny Snell And now you'll get the Devin Bush. All right fifth and final box coming up Good luck everybody Good luck little Dodger's Angels preseason actually angels at 5-1 I am Mike Towers said I thought that wax party graphic was familiar. Yeah, check out the details of our wax party Chrome all on Jasty's case breaks.com check out the list of boxes were given away. We're giving away a party invite at the end and then once we Fill the requisite amount of breaks will randomize all the names name on top is gonna win the grand prize a case a sealed case of National treasures basketball It's almost $30,000 at things, so Yeah, we got to fill a lot of breaks But it's a worthy chase and you can check out the rest of the box list as well. It's pretty nice So yeah, so the graphic we're using I think we put a Jasty's logo over it was a 1986 pack Maybe Mike Towers like it looks familiar. You got a Micah Parsons rookie ticket autograph nice Yeah, it was pretty steady today You never know what's gonna happen on any given day Rex Could be could be busy one one Sunday not busy the next Sunday. Who knows? rookie ticket autograph Jacob Harris For the Rams that's gonna be for Neil Super World Champs We got a Corey Davis to 199 season ticket.  It's a lot of money. You sell the sealed case or Do you maybe Maybe open a box or two 12 out of 49 Christian Barmore Christian Barmore that goes it's gonna go to Matthew and the Patriots We have one more coming up. We got a die-cut autograph. That's pretty cool. I don't think I've seen one of these 47 out of 75 Elijah Vera Tucker rookie ticket die-cut autograph That goes to Jonathan K and the Jets It's pretty cool There's Aaron Rodgers right there and there you go gang. We'll do a quick little Recap in a moment sure there weren't any cards next in the kid reporter cards I guess yeah, I guess that's that is this the latest version of the ticket stub. There's a wide receiver Greg little All right, so we need Two different. What are we giving away here a wax party spot? So we need two different lists. There's the new dice There's one list So the first list will be the left right randomizers for those round number of cards and The second list will be all of your names name on top gets a wax party spot Which is in our break schedule tab if you click the happy the happy party face There's someone's gonna be right here. All right, so one dice roll both lists. It's gonna be eight times six into two Side on top. We'll get them one two three four five six And two more times seven and eight seven Eighth and final time. It's gonna go to the right side. So all of the All of the right side round numbers cards will get those Six into two eight times for all of your names name only one winner name on top gets into the wax party And a chance at a case of NT basketball one after eight two three four five six seven and Good luck everybody eighth and final time drum roll drum roll Lot of sad times here, but the good news is and here's the worst spot of my apologies to Alan Very close, but we'll get him next time there and there's a lot of next times We got to feel we got to do a lot of breaks. It might take us the better part of the month, but I think it's it'll It's a worthy chase check out the promo on jasky's case breaks calm Check out the entire list of of what you could possibly win especially that grand prize. All right Congrats to Jesse With the spot that you won in a filler your names on top and you're in the wax party You've got a shot at a at a really nice grand prize.  It's pretty important. We got that done. That's wide receiver Greg little There you have it. All right. Thanks for breaking with us ladies and gentlemen I'm Joe for jasky's case breaks calm and I'll see you next time for the next wax party break. Bye. Bye


Polygenic risk scores, PRS, have been shown to capture part of an individual's susceptibility to complex diseases that their clinical utility has yet to be established. PRS may be used to estimate an individual's lifetime genetic risk of disease, but the current discriminative ability is low in the general population. Clinical implementation of PRS may be useful in cohorts with a higher prior probability of disease, such as early stages of diseases for diagnosis or treatment choices. However, there are challenges in translating an individual's PRS from a percentile of a normal distribution to a lifetime disease risk and a weaker evidence base in application to non-European ancestry. This article was authored by Catherine M. Lewis and Yvonne Lospassos.


what's up guys my name is Michael and welcome to my youtube channel today we are going to continue talking about finwick trees so this is going to be a longer in-depth explanation about finwick trees and i'm going to actually draw out the finwick tree with you guys but basically finwick trees are used for range query same thing as a segment but the reason why we use finwick trees is that segment trees are a little bit more complicated they take o of four n space complexity finwick trees are less complicated and they're more easily to implement range queries when i mean by range query i mean by when you have like an array and you want to sum up the values between indexes one to four or like two to five stuff like that so i kind of explain most of this back in the other video if you want to check it out it's in one of the cards down below with my previous video of finwick trees but let's talk about let's actually draw out a finwick tree itself but let's talk about the time complexities of finwick trees because i didn't do that in the last video so finwick trees it takes o of n space so if i have n elements right it would take o of n to create it it takes log of n to search in a finwick tree so that's good it takes log of n to update an element in a finwick tree which is also good it takes n log n time to create a finwick tree here i have an array index from zero and i have three two negative one six five four negative three three seven two three and here what i did was i basically drew the tree here so i have 11 nodes in this tree which is one more than the corresponding values of the array that we're given so in our tree zero is a dummy node that doesn't really store anything any information of our whole array the rest of the nodes nodes one to 11 does store information it stores the prefix sum of different ranges so that's what it does let's talk about why the these nodes one two four eight ten are the children of zero so why zero the parent of two four eight and ten so let's look at this look at the binary representation of two base ten is going to equal one zero so two to zero two to one yeah as a base two and if i were to flip the rightmost bit so the rightmost set bit is this this one this value of one right this is this this value is the one that's set if i flip it now it becomes zero i get zero zero which represents two zero right so that's right that's our parents there look at four is binary representation so four is binary representation is one zero zero right this rightmost set bit is one and if i were to flip it and it becomes zero it becomes zero zero zero and that's equal to zero all right so that's why zero is the parent of four zero is the parent of two so that's why you drew zero as the parent of two and four and we could go on with eight and ten let's do like an eight eighth binary representation is zero zero right two which then it equals to if i flip this rightmost bit flip this this is going to become zero zero zero zero which is equal to zero so that's why zero is the parent of eight and let's look at ten zero one zero if i were to flip the rightmost set bit here i would get uh if i flip this rightmost set bit here this one to go back to zero right i'll get uh one zero zero zero base two and this is equal to eight in base ten that's why eight is a parent of ten so as you can see here this eight is the parent of ten like ten is a child of eight so that's why that's the case of here let's look at eleven binary representation eleven is one zero one one right base two and if i flip the rightmost set bit flip this this is going to get me one zero uh one zero which is ten and that's why eleven is a child of ten and if you keep going so on and so forth you're going to get all of the in draw it out you're going to get all these values okay so basically to get the parents of whatever index i'm at so whatever node for whatever node is i want to get the parent what do i do i basically just write out the binary representation of the index then i flip the rightmost set bit and that will be the parent so if i want to get the parent of ten what do i do write ten in its binary representation find the rightmost set bit flip it that gets me eight eight is the parent of ten so you could do that for the rest of these nodes okay so now that we understand where we got the parents of each individual children and their corresponding indexes let's let's fill this tree up with the prefix some information okay so guys before we get started about generating the prefix some let's note that any number can be represented as a power of two so if i have ten here i could represent ten as a power of two two to the third plus two to the first right eight plus two eight plus two is equal to ten well about eleven i could represent eleven as a power of two how do i represent eleven as power you could have it as two to the third plus two eight plus two plus one two to the zero right eight plus two plus one that's a power of ten okay you could have five as a power of two two to the second plus two to the zero okay why is that because five is equal to four plus one which is five okay so that's why any number can be represented as a power of two so basically the finwick tree uses the idea of having the powers of two as a parent to compute its next prefix some right so the parent of ten eight it uses this value to compute its prefix some of the next value let's start doing this now the first value of the node zero is a dummy node so it stores zero okay so that's why its prefix some is zero all right let's start at one now one represents one is equal to zero plus two to this is zero which is one right zero plus one is one reason why i'm saying zero is because zero is the parent of one i'm representing this as a parent okay so what am i saying here starting from parent zero the sum of the next one element two to zero is going to be stored at index one so what does that mean my prefix sum of zero the parent of zero is zero sum of next one element from index zero is three zero plus three so that's why one is going to at index one at array index one i'm going to store zero plus three because from this element of zero the next one element is going to be itself so i'm going to store three so i'm also going to indicate that the range from zero to zero is going to be stored at index one so i'm going to put zero to zero the range of zero to zero is going to be stored at index one from zero to zero i'm going to store at index one all right guys so now two what can two be represented in terms of the parent of zero it's zero plus two to the one okay so now from the sum the first two elements from the starting point of our parent of zero i'm going to sum that and store it in the index of two so what is the sum from two values from our first value of index zero three plus two right because that's the first two values at that i'm summing from the start of our parent of zero so that's going to give us five now what is the range that i'm summing from zero to one that's what i'm summing from so i'm going to put that here that's the range that i'm summing from now let's look at three three is equal to what is three equal to including the parent well three's parent is two so that's two to the one plus two to the zero okay okay so from this representation two and one starting from index two what is the next sum of the next one element all right two to the zero is one so what is the next sum of the next one element well starting from index two the sum of the next one one element is just going to be negative one okay because i'm starting from two and the next sum of the next for one element is just going to be negative one so i'm going to put negative one here so what is the range that i'm summing from okay what is the range i'm summing from starting from index two well to get to negative one it's going to be the range of two to two because i'm starting from two and i'm ending at two So that's why I'm going to put 2 to 2 here. Alright, let's look at 4. What is 4's parent? 4's parent is 0. So I put 0 plus, uh, how do I represent 4 in terms of 0 of its parent? That's 2 to the second, okay? So now, starting from index 0, what is the sum of the first 4 elements? That's what I'm going to store at index 4, okay? So now the sum of the first elements starting from 0, starting from 0, the first sum of first 4 elements, 1, 2, 3, 4, from here to here, okay? That's the sum of the first 4 elements. That's going to be equal to 3 plus 2 plus negative 1 plus 6, 10. So I'm going to put 10 at 4. The range that I'm summing from first 4 elements starting from 0 is going to be between 0 to the index 3. That's what I'm going to put here. So what is 5 equal? 5 is equal to what is the parent? The parent is 4. Terms of representation of 2, that's going to be 2 to the second plus 2 to the 0, okay? Because 5 is equal to 4 plus 1, okay? So now, starting from index 4 at index 4, what is the first 1 sum starting from index 4? So from here, the first sum, okay? From index 4, that's just going to be 5. So I'm just going to store 5 at index 5. So I'm going to put 5. And what is the, in terms of the range I'm summing from? That's just going to be 4 to 4, okay? Because at index 4, the range I'm summing is just going to be itself. So index 4 is going to be 4 to 4. Let's look at 6. What is 6 parent? 6 parent is 4. We represent that as 2 to the second. 2 to the second plus 2 to the first, okay? Because it's 4 plus 2 is equal to 6. So starting at index 4, right? What is the sum of the next 2 elements, right? The sum of the next 2 elements. The reason why I'm looking at the next 2 elements is because that's what this is equal to, right? Next 2 elements starting at index 4. What is that? So starting at index 4, that's going to be 5 plus 4 and that's going to give us 9, okay? So I'm going to put 9 here. And what is the range between that? The range is going to be between 4 to 5. Let's look at 7. What is 7? 7 is equal to, its parent is 6. So that's 2 to the second plus 2 to the first, which is 6. Then we need to add 1, so 2 to the 0, okay? So what is the next 1 element from starting from index 6? Okay, so starting from index 6. What's the sum of the next 1 element? So starting from index 6. Our index 6 is negative 3, okay? So index 6 is negative 3. So the next sum of the next 1 element is just going to be negative 3, okay? So that's going to be negative 3. And the range is just going to be 6 to 6, okay? So let's look at 8. Starting from 8, 8 represents the parent of 8 is 0. So we put 0 here, okay? So let's represent 8 in terms of its parent is 0. 0 plus 2 to the third, that will give us 8, okay? So the sum of the values of the next 8 elements, 2 to the third, what is that going to be?  So basically we're summing up from next 8 elements starting from 0 is going to be here, up to here, okay? So that's going to be the sum from 0 to 7. And then if you put all these values in a calculator, which I'm going to do right now, that's going to give us 19. So let's look at 9. 9 is equal to 8 plus, let's just put 8 plus 2 to the 0, which is 1, okay? I don't feel like writing the binary equivalent of 8. But yeah, because 8 is, we got 8 from the parent, okay? So now starting from index 8, what is the next sum of the next 1 element, okay? So from index 8, the sum of the next 1 element is just going to be 7, okay? So that's going to put 7 here. And that's going to be the sum between 8 to 8. So we got 10. 10 is equal to 8 plus 2 to the 1st, okay? Because 10 is equal to 8, 8 is the parent of 10. So yeah. So now what is the sum starting from index 8? The next sum of next 2 elements, okay? So the next 2 elements is going to be, the sum from starting index 8 is going to be 7 plus 2, which is going to give us 9. So for 10, we're going to put 9, okay? So now the next 2 elements for 8 is going to be 9. And that's going to be the range of 8 to 9, the sum between the range of 8 to 9. All right, now let's look at 11. 11 is equal to 10 plus 1, which is 2 to the 0, okay? So now the sum of the next 1 element, what is that? Starting from index 10, starting from index 10, the next 1 element is just going to be 3, right? Because there's nothing after, we're at 10 right now. The next 1 element is just going to be 3, okay? At index 10. So that's just, we're just going to put 3 here. And that's just going to be the sum between 10 to 10, okay? All right, so that's basically summing up all the values here. Okay, so this is not the most efficient way of creating the tree, but it was a good way to explain to you guys and show you guys and draw it out of what I did to create the tree, okay? So let's say I want to start searching from ranges between 0 to 5, okay? So where do I start searching first? I should actually start searching at index 6 because 6, as you could see from our node of 6, it is the last time we restore an index of 4 to 5, right? So if I want to start summing for 6, I just take the value at index 6, which is 9, and this 9 is for the ranges from 4 to 5. So now what I'm going to do is I'm going to get the parent of 6 and the parent of 6 is going to be 4. So I'm going to add whatever value is at index 4, so I add by 10. So now that I add at by index 4, I'm going to get the parent of 4 now and that's going to be 0 and the value at 0 is going to be 0, so plus 0. So that's going to give me values of 19. And if you want to look at the ranges, for 9 is 4 to 5, for 10 is 0 to 3. So you're going to have this one 0 to 0. So then you're going to have 0 to 5. This range is going to be 0 to 5, okay? So if I draw it out, you could be, look at this 4 to 5. 4 to 5, sum these up, right? And then if you sum from the parent of 4, which is going to be 0 to 3. So you sum up 0 to 3 and then 0 to 0. So then if you look at this, this whole sum is just going to be 0 to 5. If you look at the whole sum, it will actually sum up to 0 to 5. So yeah, and to get each individual parent, all you have to do is just flip the rightmost bit that's set for like the bit of 6. I'll just flip the rightmost bit and that'll give me the parent of 4 and then for 4, rightmost bit, I'll flip it and I'll get the parent, which is at index 0. So yeah, that's how you would get the searching for the sum from 0 to 5. So let's say I want to start summing up. I want to find the sum between ranges 0 to 9. So the index value of 0 to 9. So what do I start looking for? I first start looking at index 10 because at index 10, this is index 10, right? It has the ranges of 8 to 9. So that's going to help me find the sum of all the other values from 0 to 9. So what do I do first? I look at the value at index 10. So the value at index 10 at index 10 in our tree is 9. So I'm going to first write the value of 9, the value at index 10 down 9. Then I need to find the parent of the value at index 10. Okay? The value at index 10. So what is the parent of 10? The parent of 10 is 8. So I'm going to sum up the parent of 10 and sum of that value of index 8. So that's going to be 9 plus 19. So now once I've finished the value at index 8, I'm going to sum the parent of 8, which is going to be 0. And the value at index 0 is going to be 0. So 19 plus 9 plus 0 is going to be 28. And if you were to draw this out, the range is 9 at index 10, right? This range is 8 to 9, right? At index 10, the range is 8 to 9. From the parent of the value at 9 of index 10 is going to be 8. And let's look at the value of 8. The ranges of 8 is 0 to 7. So we're going to do write 0 to 7 here. And then if you were to draw it out, this was 0 is 0 to 0. So basically, if you want to draw out this actual sum, 8 to 9 would be this here to here, right? And then 19 would be the sum from 0 to 7. So that's here, here to... And if you were to sum these two up, that will get you to 0 to 9, right? If you add these two values up, this value and this value will get you 0 to 9, okay? Let's say I want to find the range sum between 0 to 6. Well, what is the 0 to 6? The next value, the next value is 7. So I'm going to start at index 7, okay? So index 7 is the sum of... At index 7, I have negative 3. And negative 3 is the range between 6 to 6. So now I have to go to the parent. What is the parent? The parent of 7 is 6. So now I'm going to add the value of 6, whatever value I add at index 6, which is 9. So I'm going to plus 9. And this is the range between 4 to 5, okay? And now I need to keep going up to the parent, add to the parent also. So what is the parent of ranges of index 6? That's going to be 4. At index 4, the value at index 4 is 10. So I'm going to add by 10. And add by 10, then the range at index 4 is 0 to 3. So I'm going to put 0 to 3. And then now I'm at the parent, which is the root is 0, okay? 0 to 0. So now if you were to sum these up, you would get 16, okay? So now if you were to draw this out, 0 to 3 is this sum, 0 to 3, okay? And then now 4 to 5 is this sum, which is the 9, the 4 to 5, okay? And then 6 to 6 is just 6. So now if you look at this by itself, if you sum all these individual segments up, you get 0 to 6, right? If you add all this value, this segment, this segment, and this segment, you get a range from 0 to 6. So what is the worst case scenario of going through this tree? The worst case scenario of searching is going to be the height of the tree. And that's going to be at worst case log base 2 of n. So let's go back to the idea of how to get a parent of a certain node, okay? At a certain index. Let's say I want to get the parent of 11. So 11 in binary is 1011, okay? So remember, to get the parent, the parent of the current node you're at, the current index, you have to set the right most significant bit back to 0. So that's 1011. I have to set it to 0. That's 1010 and that gives us 10. But how do I do that? One way to do it is actually just to get the 2's complement and with the original and then subtract from the original. So if I want to get the 2's complement of 1011, what do I do? I just flip all the bits. So I get 0, 1, 0, 0. I add it by 1. So then I get 0, 1, 0, 1. Then I have to end it with the original. The original is 1011. The original of 11 is 1011. End it with 0, 1, 0, 1. And this gives us 1. True, true is true. True false is false, 0. True false is false, true false is false. That gives us 0, 0, 0, 1. And then now I have to subtract 0, 0, 1 from 1, 0, 1, 1. 1, 0, 1, 1 minus 0, 0, 0, 1. And that gets rid of this last bit. This last bit now gets set to 0. So that gives us 1, 0, 1, 0. Which base 2 is it going to equal to 10? Okay? From base 2 to decimally, it gives us 10, which is actually the parent of 11. So this is how you do it programmatically. In the program, you just flip all the bits using the not symbol. And then you end it with the original, then subtract from the original. So if you wanted to do it programmatically, that's how you would do it. Okay? Because there's no real possible way to do it to set the right, to get the right and the most bit and set it to 0. So that's what you have to do. So the time complexity of getting the parent of a single node in our FinWikTree is going to be 0 of 1. Because it will only take 0 of 1 time. Constant time to get a certain value, to get a parent of a certain value in our tree. Okay? All right, guys. So now let's figure out how to do this efficiently using the parent instead of recalculating over and over again to generate our FinWikTree. Okay? All right, guys. So what I did was I basically just redrew the whole tree and put all the values with zeros. Okay? So the same thing, put all the values with zeros. So a more efficient way to do this is actually to use this function called getNext, which is you're going to get, whenever you update an element in your FinWikTree, you are going to propagate the changes to the next node that's going to get affected by your previous change. So that's what this getNext does. So to get the next node that is propagated from your change, you would use something called getNext, which is what you do is take the two's complement, you end it with the original, and then you add it to the original. Okay? So that gets you the next node that would get affected by the change that you just made. Okay? So let's go back to the original value. Let's start from zero. Okay? So zero, the first element that we're going to sum up from zero is three. Right? So we're going to add three to our first value. So let's change this value. So three, okay, but this is just not enough. Right? We have to propagate the changes to the other nodes that would get affected by changing this value to three. So let's get the next value of our index of one and propagate those changes to the next value. So our index of one is, if you write it in binary, it's going to be zero, zero, zero, zero, one. I don't know if zero is a tag on. Okay? Let's get the two's complement. So that's what you do is you flip all the bits, one, one, one, zero, and then you add one. So then plus one is going to be one, one, one, one. So now we're going to end it with the original. So when you end it with the original, you get zero, zero, zero, zero, and then one. Okay? Now we're going to add one to the original. This is the value we have to add it to the original. So we're going to add this to our value one. So zero, zero, zero, zero, one plus zero, zero, zero, zero, one. This is going to give us zero, zero, zero, one, zero, two to the one, which is going to equal two, two. So our next value we're updating is two. So now we're going to change at index two to become three. So that changed that value. And then we have to propagate the next value of two now. So let's do that. So if you continue doing this function of adding, getting the two's complement and ending it with the original, adding it to the original. If you do the next value for two, you'll get four. And then four, you'll get eight. So then let's propagate those changes to a four and eight. So let's just do that. So here, let's make this. So yeah. So at eight, if we get the next element of eight, we actually end up getting greater than 11. So we end there. Okay. So the next of eight, we end there. So we're not going to keep going. Propagating. So the amount of time it took to update all the values of three is going to be O of log of N. If you just count the number of times it took. All right. So now let's look at the next index that we're going to update, which is one. So at one, we'll look at index two. And then now we're going to add the values of two to whatever was currently at two. So that's going to do three plus two is going to be five. So now I'm going to set this to five. And then I'm also going to propagate the changes using the next function, which is going to be four and eight. So this is going to be five. Okay. And then when you hit eight, eight's next is greater than 11 the size of our finwick tree. So then we stop. All right, guys. So now let's look at index two index two is negative one. So what we're going to do is we're actually going to go to index three and set the value to be negative one because three is a range of two to two. So that's why we're going to set three is going to equal to index three. We're going to set to negative one and then we're going to find the next value of index three. So if you were to actually calculate yourself and you would actually get four. So three's next is actually four. If you follow this formula, I don't feel like drawing it out again, but three's next is basically four. So then now what we're going to do is we're going to add negative one to whatever value was at four and update those changes. So that's going to be negative one plus five, which is going to be four. So we're going to change this to be four. And then now we have to propagate the changes. Four is next is eight. So then now we have to also add negative one to the value of eight. So this also becomes four. So now we're going to go to the next index that we're updating. So last time we did two and we're going to go to three now. So now at three, what we're going to do is we're going to go to the next index, which is four. So now at index four, we're going to add six to it. So we're going to change this to become four plus six is going to be 10. So this is going to be 10. Okay. And then now we have to propagate the changes to the next element of four, which is eight. The next element of four is eight. So now we're going to prop add six to eight also. So this is also going to become 10. So now we're going to go to four now and we're going to add the value. So the range of four is four to four. So that's at index five. So we are going to just put five at index five. So yeah, because the sum of four to four is just itself. So we're going to put at index five or just put five because that's the value of our array. So now if you were to apply the same formula to five, fives next is actually six. So we're going to change six to become five also. So then six next using this formula is eight. So now we have to propagate our changes of six into eight. So then now we're going to add five to whatever value at eight. So it's going to be five plus 10, which is going to be 15. So now we're going to add whatever value at go to the next index. We're going to go to add value at five, right? So now we're going to go to whatever range that effects. So that's that'll be six, right? So five, we're going to go to six and we're going to add whatever value at our index five into six at index six. All right. So then four plus five here is going to be nine. So we're going to change six to nine. All right. So six is next is eight and so we have to propagate our change from the next of six. So that will be four plus 15. So that'll be 19. So now we're going to change eight to become nine. Now we're going to update at index six. If we look down here, uh, index six is five to six. My bad. This is supposed to be six to six. So yeah, six to six, it'll be minus three because it's the value of six seven's next is also eight. So now we have to add negative three proper propagate to change the negative three into our next value of eight. So we have to do 19 minus three, which is going to change to 16. So now we're going to update seven. Uh, so we're going to go to index eight and then because there's a value index eight, we'll just add three or current value at seven three to whatever value eight. So 16 plus three is going to be 19. Now we're going to add the update the value of eight of the index eight. So we're going to check the index of nine. So index nine is just the sum of eight to eight. So that'll just be seven. Okay. So this is going to become seven because that's our value eight. All right. So nine's next node is 10. So 10 is going to also become seven. So let's change that. All right. So 10's next is outside the range. So we don't update that. So now let's go to we're going to update nine. So how do we update nine? We're going to go to the 10th index. So at the 10th index, there's a value here. So we're going to up we're going to add two to the value of at this location. So this is going to be two plus not a seven. It's going to be nine. Now we are at the final element of our array of index 10. So we're going to go to 11. And 11 is just 10 to 10. So we're just going to add three and then 11's next is outside the bounds. So we don't continue after that. So yeah, that's pretty much it. All right, guys. So now that we're done because to update each element of the in the Finwick tree is log of n time, right? A log it takes log of n based on the tree going down to the tree. And then because we have n elements in our array, it'll be n times log of n to construct our Finwick tree. All right. So let's think about what would happen if I want to update a value. So let's say I won't add next three and then I want to update it to nine. So so what am I going to do? Well, the difference between nine and six is three. So that's a plus three difference, right? So that means that for all the values, I'm going to have to change it by a difference of three. Okay. So now at I'm going to go to index four in our tree, which is this four and I'm going to add three to it. Okay. So I'm going to add three to it. This is going to become 13. Now I have to update the next value of four. So that'll be four is next is eight. So now I need to change eight by adding three eight. So that'll be 19 plus three is going to be 22. So now it's next is outside the range. So it's done and the amount of time to update an element would just be of log n because that's the height of the tree to update an element. So yeah, let's go over another example. Let's say for we're going to update four. So to do that, let's say we are going to change five through six. So five is going to become six and that's going to be a difference of plus one. So now we're going to go up to index five, right? And we're going to add one to it. So it's going to be five is now going to become six five plus one is now going to be up six. And then now we have to update the next of five. So that will be who fives next fives next is six. So now I have to add one to fives next up six. So nine plus one is going to be 10. So let's change this to 10 then six next is eight. So we have to add one to whatever value at eight. So then now we're going to change 22 to become 23. So yeah, so the amount of time it would take to update this whole thing like tree would be of log n because you're just going to the next element and change it. So yeah, that's all we have to talk about. Finder trees rate comp subscribe. I hope this is a good in-depth tutorial. Check you guys later. Peace.


The Senate has reached a resolution to abolish aid limitations in job advertisement. The senator representing Benway South's Senatorial District, Abba Moros, points out the motion on the floor of the Senate. He said such discrimination is in contravention of the Chapter 4, Section 42, Subsection 2 of the Constitution of the Federal Republic of Nigeria. He drew the attention of senators to the provisions of the International Labour Organization, that probably beat age placement in the advertisement of job opportunities, adding that discrimination by aid bracket has denied lots of potentials that will have contributed positively to the economy, insisting that Nigeria cannot be different. After the debate on the motion, the plenary resided over by the Senate President, Gautre Le Paveo. The Senate adopted a resolution calling on the Labour Ministry to redraft policies abolishing age limits in job advertisements. Ironically, that a graduate in this country can serve in the National Youth Service Corps programme at age 30. They cannot be gainfully employed thereafter on the fact that he or she is above 30 years, a situation that is a flagrant breach of his fundamental human right. You cannot order the Nigeria laws imposed on an employer, policies which regards to age. However, in the Nigeria labour statutes, it is clear that once you are up to the age of 18, you are employable. But the decision to employ, whether you are 18, 19, 20 or 40, is the discretion of the employer. Ironically, that a graduate in this country can serve in the National Youth Service Corps.


The Midget State University hosted a guest speaker from Western Illinois University to talk to students about societal issues. The Toxic Masculinity Lecture was a two-day event where students discussed issues about masculinity, gender, and identity. During day two of the event, the speakers met with student athletes and students involved in leadership for lunch. The guest speaker says toxic masculinity comes from how society perceives how men should behave. There are particular images of masculinity that if men were to adhere to them rather than authoring them themselves, it becomes problematic, it becomes toxic. So toxic really means that kind of masculinity that you assimilate to based on some external standard as opposed to authoring it yourself. Tracy Davis says he was impressed with the quality of conversations that students at BSU engaged in. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Hello there, I'm Sandy Allnock and I am a full-time artist living just south of Seattle, Washington in the United States. I have been doing this full-time since 2013 when I quit my career as a graphic designer and illustrator. I love to be inspired by nature, whether it's working from photographs or going outside and painting out in the mountains in the beautiful area that I live in. The part I love the most is teaching other people and helping them to grow into their own careers as artists. So I do hope you'll join me for this class. It's going to be a lot of fun and I'm excited to get busy painting with you. Thank you so much for joining us today. So just a quick check if you can hear us and see us okay. Please type Lama in the chat just like I'm showing right here. And let us know where you're viewing from. Let us know how is it there. I see some people typing in that it's a bit chilly where you guys are. Well, it's a bit humid where I'm at. We are really different from different parts of the globe. How is it where you're at Sandy? It is cloudy and cool but I am hoping it's going to stay dry because I got to mow the lawn today. How do I already have to mow the lawn when it's not even April yet? Oh my gosh, climate change I guess. I see a lot of llamas in the chat. Hello everyone. Okay, we've got from Belleville. We've got from London. Amazing.  So I guess we can begin. So hello everyone. I'm Kathleen. I'm with Etcher Studio and I'll be your host for today. I will be while assisting Sandy right here. For those who are new with Etcher, we are an art learning platform who works with our teachers from all across the globe. And today's free demo is brought to you by Sandy Alnok. And this works as a preview for her 90 minute class. That's going to be on May 1, 2pm Eastern time. And I'm going to be dropping that link in the chat. Hello from a cold and partly snowy Sweden. Oh wow. Pretty interesting then. I'm glad we don't have snow here. I'm glad we don't have snow. Yeah, we'll take that anytime. And speaking of the 90 minute class, she will be talking about how to do watercolor textures, layers, negative paintings, to make a nature inspired, well, nature is seen, not nature inspired.  So you might want to consider having a look at that. So before we begin, if you have any questions for Sandy, I'll go ahead and drop the format in the chat how you would be needing to type them. We could type them in all capital letters. Also, we have a private Facebook group open to anyone making art related to both our free content and paid classes. I'm going to be also dropping that link in the chat. Hello from Seattle, Florence, Italy. People are already coming in. Okay, so with that said then, I'll go ahead and pass things over to Sandy. Can you let us know what you'll be doing today and how that connects to your etcher class? Sure. Today, we're going to be just talking about color. And I wanted you to have a chance to spend the month before that May 1 class getting to know your colors in a different way. So I have developed a whole way of swatching. And I've made myself a swatch book that is growing and getting bigger over time. And I'm going to show you how to do that. The way that it relates to the class coming up is that we're going to be painting trees. And you're going to need to know how to mix some greens and some browns and grays based on the colors that you have in your palette. You don't have to have my colors. I'll certainly tell you what they are, but you can have your own colors and learn how to mix them in your own way. So let's get busy painting. Great. The class that we're doing today, as I said, is just going to be swatching. So there's no reference photo or anything for it. And the painting that I just showed you that we're going to be doing in the class, I also have done in a sketchbook format. So you're going to see more of this sketchbook later on in this presentation. I'll be able to share some of the other paintings that I've done in this accordion book.  Of course, water. I love this Goodwill jar that I got from my water. And I'm going to be putting mine on a ring, but you can also put them in a book. You can leave them on sheets, whatever way works for you in having your swatches. So if you've never used a watercolor block before, this one is a cold press block. And it's got glue basically all the way around all the outside. So I'll show you in a little bit how that actually matters when you try to get to the next page. But we're going to talk a little bit about color theory and then get to the color mixing. In color theory, there's all different kinds of words you can use to describe colors. And warm and cool is one of them. So I've made myself a color wheel that has warm colors on the outside, cool colors on the inside, so that I could just get a general comparison of what those are. There's no science to say you have to have this particular color for a warm and this one for a cool or anything. There just are some colors that are warmer and cooler. And I've got a palette that I put together with warm colors on one side and cool on the other just for teaching and examples and that sort of thing. So when you make any kind of a color wheel, you need a red, a yellow, and blue. Those are primaries. And you can see the difference most clearly with the warm and the cool in the yellows. Someone in the reds, you get more of a tomato versus a cherry red when you talk about warm versus cool. It's really hard to tell with blues. There's people, artists all over the world who fight about what is warm and what is cool. But we'll leave all that aside because the temperature doesn't really matter as much as the results you get, right? So the outside that I did here is the warm colors. The inside is the cool colors. And you could see the difference in the kinds of colors that those warms and cools will make. That's the one place you want to know the difference between them. So the three primaries are separate from each other, equidistant around the color wheel. Everything halfway in between are secondary colors. And then there's tertiary. And you could actually do this like 27 levels down and keep making color mixes. But we're going to stick with things like an orange that's made out of yellow and red, a purple that's made out of red and blue. So those are your secondary colors, the ones to keep in mind for the rest of this class. So I've got the cool ones on the inside, warm ones on the outside, but that doesn't really matter. Didn't I tell you that already? Neutrals are how you get to them is by taking the red, the yellow, and the blue and mixing all three of them together. Now here's where I said get rid of that page on the block. I just stick a ruler under it or a pencil or a knife or something. Sometimes it's easy to tear the glue. Sometimes it's a little harder. So that is how you use a block. You just don't have to tape it down, which is nice. So let's talk about those three color mixes, the red, yellow, and blue. I've divided my paper into two inch strips and then horizontally across the page. I find it's easier to do this without cutting all the paper into strips first. And I'm going to show you what it looks like to mix a red, yellow, and blue and you get a neutral when you mix all three colors together. And sometimes they make a baby poo color and sometimes they make a nice gray or a nice brown. Really depends on how much of each color you put in it. So here I've mixed out of the warm colors, something that looks kind of gray. If I add a little more red to it or a little more yellow to it, I can make a color that's more brown. And if I want to push it back toward gray, I can add more blue to it. And you can get an infinite variety of browns out of colors like this. I could do the same thing with the cool colors, with the blue, the red, and the yellow in varying amounts of each other. And see what comes of that. It's really difficult to make this mix over and over and over again and get it consistent though. So as you can see, just one little dollop of red is going to totally change the color. And once I add a dollop of this particular blue, it's a phthalo blue, it's really strong. It goes immediately to gray. Well, how do we control all that? Because there's so much to think about when you've got three colors to mix. Well, I thought let's talk about making the same kind of mixes, but with two colors instead. And that's what my whole ring full of colors is. These are all two color mixes, but look how many colors I get out of each pair of colors that I decided to swatch. So I'm going to show you how I did that and how you can do it as well. One of the best places to start is complementary colors, colors that are opposite each other or just barely opposite each other. So opposite or neighbors to opposites. And the reason that that works is because you'll end up with one color that's compound, one color that's a single color. So say this purple color, it's an imperial purple. It's got a red and a blue in a purple. And you mix that with a color that's yellow and you have your red, blue and yellow all together. In my swatches, I've mixed them in various levels of mixes and we'll talk about that in a minute. But here's another example, lunar blue that has a little bit of yellow in it. The yellow orange or the yellow ochre, excuse me, has some red and yellow in it. So between that, you get red, yellow and blue, but you're only mixing two colors. So you don't have to fight with that third color. Here's moon glow with ariolan moon glow is a purple, but it's a really dull purple. And you add a really bright yellow to it. You can get a really nice gray. And here's one of the crazy ones that just seems like it shouldn't make sense. Green appetite with quinacridone rose. It's a pink and a green and you can get neutrals out of it. So I've taken both of my palates and I'll be working with both of them during this demonstration. So I've put the the earlier swatch that I made over to the side and we're going to try to see if we can replicate that. I put a dot of each of the two colors at the top of the swatch and after it dries, I'll add the color names to it, just indications of somehow that I'll know which colors they were. And then I want to find out what is the most natural mix that these two colors make. Like if I was just not thinking, putting in some purple, putting in some yellow and not really worried about what measurements of each one, like how much of each color, what color does it want to make? There's some combinations that are going to want to make a grayish color. Others are going to want to make a brownish color. And still others, depending on the strength of the pigment itself, whether it's as my friend Lisa Spangler says, it's a bully or not, the bullies can force a color mix into one direction because it's a really strong color. But here we've got the imperial purple with new gamboge. Crazy kind of an idea to mix purple and yellow. It's one of my favorite things to do because I get so many variations on neutrals. I dipped my brush in water so I could see what it makes as a mix when it's really pale. And then for those two small swatches in the middle of my swatch cards, I'm actually doing a mix on the left hand side that's mostly purple and just a little bit of yellow because that's going to tell me if I use that color and I want to dull it down a little bit, I can put just a little bit of the yellow in it and know what that makes versus using a little bit of purple in a bunch of the yellow. So this little swatch card is going to show me a lot of information about that color mix. And I'm going to know how I got there or at least mostly how I got there. That strip along the bottom, I decided just for fun to see if I could push colors to become almost black. How dark could I get them if I really worked to get most of the water out of it and make it mostly pigment? Excuse me, could I turn it into a really dark color of some kind and what kind of color does that make? Well, you can see the difference between my original swatch and the new one. They're a little different because you can never mix the same color twice exactly perfect. That's just not going to happen because that's that's what painting is all about. However, you can get a good idea of how much of each color can push it in one direction or the other and that sort of thing. So let's try another crazy combination, purple and green. These are not compliments because the purple has blue and red in it and the green has blue and yellow in it. You've got all three colors but these two make almost automatically they just love to make a gray. It's the strangest thing but I found it out because I was testing and you won't know which colors of yours do that until you test your colors in your palette. So I've watered it down so I can see if I can get a sidewalk color or a building color out of that a tree trunk or something and then did my mixes so I get a mostly purple with a little green and mostly green with a little purple and then I wanted to see what would happen and this is the super magic. If I use straight up perling green and straight up imperial purple together it makes black. It's amazing what a nice rich black that can make and you can use these colors in combination not just mixing them in your palette. If you're painting something and you want to make it go black now I know which color to mix with imperial purple if I want that imperial purple to go practically black. So let's try another combination and this is another one that is one of my favorites for making neutrals. Any kind of blue with any kind of red for the most part and this is a phthalo blue and anthraquinoid scarlet and these two almost immediately will make some kind of a neutral without even thinking about it because they just cancel each other out. The phthalo blue is a super strong color so you have to be a little bit careful how much of it you use and if you have it in your palette you'll probably know that it takes over it's the bully color it it wants to dominate that red and turn it into anything but a red. Now if I use more of that phthalo blue look what happens when I just add just a little tiny bit more of it it goes really blue. When you start testing the colors in your palette whatever's in it and don't feel like you have to go get my colors you're going to find out which colors are the bullies because if you try to make a 50-50 mix of something the bully will immediately make itself known the one that wants to take over and there's not always going to be a bully in every pair there's some that just naturally are going to work in in making a neutral mix it's just the the way things go but there's some colors that are immediately going to tell you I want to be in charge and you'll know when you start making a mix and you add that color you need to add less of it if you want to get something more neutral rather than letting that color take over so which pairs are the best ones you should swatch well you could swatch anything of course but I would recommend not going with those primaries necessarily do the compound colors the ones where you have a green that is a blue plus a yellow or a brown that's usually a red plus a yellow but a straight up yellow is not going to be all that helpful all the time except for when you're mixing it with one of those compounds pardon me get a drink of water here talking too much so we have cascade green with alizarin crimson now I happen to know alizarin crimson is one of my bullies it just absolutely loves to take over and look how how much it eats away at that cascade green because I had so much of it in the palette so I'm going to add some more of the cascade green when I use these two to make a neutral gray I already know immediately because I've used it enough that I should add more of the cascade green and less of the alizarin crimson and once you start doing these kind of practices you'll know that if you love the color that it makes but with one as the primary one is the secondary this is the place to work that out and as I'm doing here you can do smaller cards you don't have to do the whole swatching with the the majority and minority types of swatches in there you don't have to see what it does trying to go black with it you can do just single squares and see what those two colors do together and make it simpler on yourself and here I'm using another mix of a blue and a brown now I only have one brown in my entire palette and this brown is transparent red oxide it's very close to a burnt sienna and I use burnt sienna a lot in a lot of my videos so many of you may have that you can use that instead but what I decided was to see what I can turn that one brown in my palette into with all the different colors that I have in my palette what can I do with that one brown because then I don't have to actually own a whole ton of browns when I first started watercoloring I thought I had to have all the colors and I have so many palettes in a drawer that I never use because I felt like I had to have that color I didn't know how to mix it and once I learned better how I could mix the colors I keep in my palette are ones that make nice mixes with others so I can keep one brown and just keep mixing it with different things mixing this with a green seemed crazy to me but it makes the most beautiful orangey kind of color it's quite nice you can mix a more granulating type of color with it you can mix colors that have different properties in them and change the entire tone of that brown you could do the same kind of a thing if you have a favorite gray color mix it with all of the different colors of your palette and see what happens with them and this will also inform you as I said before of what's going to happen if you drop a color wet in wet into another one I've done a lot of landscapes in which I use primarily a moon glow which is a purple with a yellow ochre which is a yellowish color and the whole scene feels very brown and very neutral and very vintage but I knew that because I'd played with those two colors together and until you start playing with your colors you won't learn those lessons and know how those things are going to react on paper and speaking of which when you do your swatching it's really helpful to do them on the kind of paper that you're going to be painting on so don't just opt for the cheap paper because you're just doing testing necessarily you can certainly do some initial tests but if you're going to have some swatches you keep make sure those are on the kind of paper that you love to paint on so that you know exactly how they're going to turn out when you are doing your painting itself so these are all the finished swatches I eventually made for the transparent red oxide look at all this I mixed them with every single one and one of my favorite mixes was transparent red oxide with panes blue gray because you can push that real easily to a gray or push it real easily to a brown and I wanted two cards with it so I could know what colors were available then out of that that pairing now this is a little bit of a crazy this is me and my weird color science I wanted to see what colors of neutrals would be good for things like tree bark and I categorized all the tree bark that's out there that I could find on the web there are some that I put in the middle that are more true neutral grays for the most part there were some that I found that had an orange tint to them some were heavier orange really strong orange color in the bark and some had just a tint or a wash of orange the reds there are some bark that is just really really red some has a pink cast to it so all of these different browns and neutrals that you're mixing are going to have a use if you paint a lot of trees there are some barks that have yellow in them a yellow tone to the colors and you can have some that have green a tint of green sometimes it's the bark color itself sometimes it's moss or sometimes it's reflections off of other things in the scene around it there are blue greens I found some wood that has actually like turquoise to it which was amazing and I wrote all these down put all the color names because I want to go paint each one of these in my big accordion sketchbook because it's really fun to think about all those colors in there there's even violets and blues so all of these color swatches are going to help me every time I try to do some color matching if I want to try to find a particular green from a particular tree I can make all the green swatches in the world I can take all these combinations and see which ones make interesting greens and they may not be greens they may not have a green mixed in them it's hard to say until you actually do this watching and see what happens when you mix different colors together but you can get all kinds of varieties just by mixing two colors instead of stressing out about three as long as you have some red some blue and some yellow in whatever the combination is that you're mixing you'll get a neutral of some kind and if you don't worry about having all three you can get greens you can test for purples all sorts of stuff so here's that accordion sketchbook and it I've just been painting trees in it just trees tree trunks and I want to fill this I've got pages and pages and pages I've been putting even more in this since this this moment of opening this sketchbook I am just loving practicing with all of the different colors that I've already tested out and seeing what else I could create with them and I hope that by the time we get to the class on May 1st to paint this scene that you're going to have practiced your browns and your grays and your greens so that we're going to be able to do that painting and use a lot of those combinations in a real-life context so how many of you are thinking you want to go get busy swatching now I have a feeling Kathleen's going to be doing that oh gosh yeah I was telling Sandy earlier it's midnight where I'm at but I'm going to spend the whole evening just do or at least I'm from the future now to do some swatching and I can guarantee you that it's going to be the same for our audience I've got a lovely comment right here from Sue saying all beginner all beginners need to see this before hoarding all the colors speaking from experience see now all of your extra money you have saved from not having to buy all that paint you could just send that to me that'd be totally fine well that would be a great idea so we could put some use to it so um great that was a lovely swatching exercise um never seen so many streams at one time I know right Sandy has um went down the rabbit hole just to like give you all of these references all in one place and so we've got some questions right here I will oh I've got a raised hand emoji I think she's down for some swatching all right so um just to confirm again I think this is from Sam will you be using the exact same palette for your 90-minute class I believe I'll be used well there's two palettes that were shown I'll be using the big palette with the big wells in it and tomorrow on my blog I'm going to post the the replay of this along with the color list that's in that palette so if you're going to be taking that class and you want to use that palette of colors you can certainly do that but as I said you can use your colors because you already have colors I know you do and you don't need to go buy my colors so gosh which I think answers my blog great great um which I think answers another question um what about color mixing with other paint brands um or is it better with sticking with just one paint brand or is does that even matter it doesn't really matter a whole lot I mean there are some brands that are higher quality brands and some that are lower quality brands if the lower quality is what you can afford then use them but you can still mix and match them any any old way it how I'll just put one caveat on that if you were to use something like opera pink opera pink is of what they call a fugitive color it disappears over time when it goes to light so if you make opera pink with I don't know phthalo blue or any other blue then eventually that color will no longer be purple it might start out as purple but it will disappear because it'll just leave the phthalo blue in there so you want to make sure you have good light fastness if you want to keep the painting for a long period of time as far as just mixing and painting use what you have and mix and match brands totally fine great advice and yeah I totally agree with that some colors are just um deceiving I guess all right we've got some more questions right here or comments rather um trying to build my art brand around it with p&w themed and inspired work and designs um and then let's see we've got I think I saw some lovely comments right here hold on let me just go ahead and backtrack with it and meanwhile if you do have final questions for sandy just go ahead and type them in the chat um I've done swatches but not your way love this method says natalie ingram thank you so much natalie um I only just came up with this recently so I haven't seen anybody else do it either but I was just really curious about how to get to certain colors and this was the best way that I could figure out to do that all right and we're glad that you found out this way to be honest it was really an amazing way um tim says love this process I've been thinking about swatching to better understand the paints I have now I have a solid process to lay them out thank you so much and um oh question from Nancy do you do this same type of swatching for other color mixes when you're not trying to find neutrals you certainly can and I've started to add to my book you saw some greens in there originally I started out I was just looking for neutrals and then I realized oh I could I could figure out more green options that I have I live in the pacific northwest or we have trees trees trees trees trees trees and the grass goes from one shade in one season to another shade in another season and I was just having a blast mixing different greens you could do the same for purples all different kinds of colors could follow through with this method very easily great um we've got oh some pretty interesting questions um I think these are both related do you ever use white and if you're mixing a black would you only use colors that are already in your painting okay good questions I don't use white very much if at all the only time that I really do would be if I was trying to do say uh what do you call it I've lost my my strings like the the wires that go across from telephone pole to telephone pole telephone wires yeah okay my my brain is slowly engaging if I were to try to add something like that or a sparkle highlight on something I might use a little but I don't mix it with any colors if I want an opaque color I have an opaque color generally to to use and I don't tend to with watercolor because I always figure watercolor is all about the transparency so I don't mess with that and what was the second question the second question was a good yeah sure um if you're mixing a black would you only use colors that are already in your painting that is one of the reasons I was testing to see what makes a black because there's a lot of times when I don't want to just add black into something I I only have one black in my palette and I rarely touch it because what I found is that it just adds a garish kind of feeling to an area if I just suddenly dollop in a black I tend to use more of a paints blue gray if I'm going to introduce another color at that point but it's much better if I'm using purple and green and I have a purple and green that coming together make a black it's a lot better to use that in a painting and limit the number of colors you have in the whole painting itself by using various mixes of what's already in there hey um you've got more I'm so glad you're reading the questions not me I bring it lost I would start getting getting lost in somebody telling me the weather there so you're oh my gosh well thank you well to be honest you're not making easier for me people are just super enthusiastic here um let's see um we've got a few more questions um what let's see I think I've lost it too now I'm lost either let's see um we've got one right here oh somebody's asking about if this will be posted in the um in this youtube um yes we will be having this posted so if you've missed the first few parts of it no worries because we'll have this um once we end the live you could definitely just refresh the page um but if not it may take quite um some time and Sandy mentioned that she's going to be posting a blog about it um about the materials someone's asking about the materials that you used um all of it is in the description below um in this video and if you want to learn more or ask more about um how Sandy has prepared her um swatching palette right here um I think it will be helpful to post some instagram stories maybe um do you think Sandy that might help absolutely I'm going to go through the questions after we're done and see if there's anything else because it's still color theory week on my instagram I have all week long I've been going crazy on color theory and I'm going to be adding more to it so I'll be answering some of your questions in that way as well as on the blog I'll have this video I'll have the supply list I'll have um also a handout there's a handout that we've been trying to figure out getting it uploaded never even doesn't get uploaded it'll be in the blog post tomorrow and it has that chart with all the tree trunks in the different colors so that you can go and research those tree trunks yourself if you want to see like what tree trunk has turquoise I now know I'm so excited oh gosh yeah it's a really completely different way on how to look at trees right now um I think we've got last question what colors do you use on the cover of your swatch book I'm pretty curious myself that is alizarin crimson with caskey green amazing all right so I think you guys are done with your questions but some of these specific questions um sandy can answer because I think this has something to do with most of the materials you used um and just wait for that blog post all right so I think we can wrap up so thank you so much sandy for that lovely demonstration and lovely um just watching exercise so everybody we do have these live demos a couple of times a week so make sure to hit that subscribe button below to subscribe um to sandy's youtube and also i'm going to be dropping the link on etcher studios um youtube so that you could go ahead and subscribe to that too and we have a subscription um so that you could go ahead and access have access to all live 90 minute classes classes including sandy's 90 minute class which will be again for the newcomers um that's going to be on may one that's 2 p.m eastern time i'm going to be dropping that link i'm going to drop a bulk link actually um first oh okay oh one last question I think we can entertain one more then so from sand um is the right thing to do uh is to take the first little palette of warms and cool reds blues and yellows you don't have to make a color wheel if you don't want to this is more about showing you why those three colors make neutrals so I wanted to show you that like the traditional thought behind why red yellow and blue make neutrals but most people aren't going to want to do that now it's fun sometimes to see if you can create oranges and yellow oranges red oranges out of the colors you have i'm not going to stop you from doing that because it's fun but you don't have to do that in order to do these two color swatches to get to know your colors because what I want you to do is know them so well that when your brush goes into your palette you know what you're going to choose and why because you know how it mixes with something else you're using amazing all right thank you so much and somebody said great for minimizing colors for travel sketching I totally agree um it's going to be a great help for them and okay so like I mentioned we do these live sessions a couple of times a week so go ahead and visit our youtube channel as well you um at your studio so that you could go ahead and check out more live classes there and also I'm going to be dropping a link to our feedback survey so if you loved how sandy has broken down all of these um seemingly complex color swatches um and has broken down to a simple way for you go ahead and um let us know through our feedback survey which I think is already being flooded so I'll go ahead and drop that link again um I'll go ahead and drop that link right here in the chat um so let us know how you thought about sandy how this demo was super helpful for you or just give us a like or leave a comment below this video and I'm going to be dropping sandy's instagram account in case you followed along today I'll go ahead and tag sandy on instagram or join our private facebook group where you could share your swatches so maybe you could have like more colors that you might have discovered so it's great to share um excellent session and before we end I just wanted to let you guys know that apart from this live um class preview sandy has also guested in our make more art podcast which was the topic earlier um in the chat so you might want to check that out hers is on episode 95 and 96 I'm going to be dropping that link right here and you're the queen I am yep I should have and while I am doing that uh do you have any final thoughts sandy before we sadly have to close the session I just want to encourage everybody to get to know your paints better and especially if you're planning on coming to the 90-minute class because I'm not going to spend time just talking about every single mix that we've got going on because we're going to be doing negative paging we're going to be doing textures we're going to be laying out an entire picture and I don't want to get distracted with that because we've got a lot of painting to do in just 90 minutes so I'm hoping that you're going to get all your practice done anytime from here until then that you have questions on your color mixing just give me a shout out either on my blog on my instagram or wherever I'll be happy to help you out amazing all right so I think we can end um apparently we have to close the session so that you guys can do your swatches so thank you so much sandy for that wonderful demonstration and thank you everybody for being super enthusiastic in the chat for being so active and for your appreciation I hope we made your day and until next time everybody make more art bye for now