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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Examples of Apache Spark SQL with user defined functions
Topic
Step2:  Compute and display the Mandelbrot set using Spark SQL using plain old-fashioned ASCII graphics for the output
Step4:  Mandelbrot in SQL, displayed with color
This computes and displays the Mandelbrot set on the terminal using color, with a blue palette.
Note
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Python Code:
# the function definition
def mandelbrot(cR, cI, maxIterations):
    zR = cR  
    zI = cI
    i = 1  
    # Iterative formula for Mandelbrot set: z => z^2 + c
    # Escape point: |z|^2 >= 4. Note: z nd c are complex numbers
    while (zR*zR + zI*zI < 4.0 and i < maxIterations):
        newzR = zR*zR - zI*zI +cR
        newzI = 2*zR*zI + cI
        zR = newzR
        zI = newzI
        i += 1
    return i
# registers the function mandelbrot as a UDF for Spark
spark.udf.register("mandelbrot", mandelbrot)
Explanation: Examples of Apache Spark SQL with user defined functions
Topic: Provide an original example of Spark SQL and the use of UDF.
The example has originally been developed for the command line (pyspark/spark-shell). It shows how to compute and display the Mandelbrot set using Spark SQL. The visualization uses ASCII graphics and a version with color is provided using ANSI escape codes.
Compatibility: this code has been tested with Spark 2.0 and 2.1
Author: @LucaCanaliDB, January 2017
How to run:
* Copy-paste the code for UDF and SQL into a Spark session running with spark-shell or a Scala notebook
* For the version "SQL with color", use a terminal/notebook that supports ANSI escape codes  
This is the Python notebook version, for more info see also https://github.com/LucaCanali/Miscellaneous/tree/master/Spark_Notes/Spark_SQL_UDF_examples_Mandelbrot
The vanilla ASCII version
UDF: The cell below defines a helper function. It implements the "escape time algorithm" 
for the Mandelbrot set visualization as a Spark user defined function. 
Inputs: cR and cI represent the point in the set/image to evaluate (c is a complex number).
maxIterations is maximum number of iterations.
Output: the function returns an integer representing the number of iterations to reach the 
"escape point" (|z|^2 = 4) or returns maxIterations if it did not reach it.
End of explanation
spark.sql(
with
    x as (select id, -2.0 + 0.027*cast(id as Float) cR from range(0,95)),
    y as (select id, -1.1 + 0.045*cast(id as Float) cI from range(0,50))
select translate(cast(collect_list(substring(' .:::-----++++%%%%@@@@#### ',
       mandelbrot(x.cR, y.cI, 27), 1)) as string), ',', '') as Mandelbrot_Set
from y cross join x 
group by y.id 
order by y.id desc).show(200, False)
Explanation: Compute and display the Mandelbrot set using Spark SQL using plain old-fashioned ASCII graphics for the output
End of explanation
result = spark.sql(
with
    x as (select id, -2.0 + 0.027*cast(id as Float) cR from range(0,95)),
    y as (select id, -1.1 + 0.045*cast(id as Float) cI from range(0,50))
select translate(cast(collect_list(color) as String), ',' , '') as value
from y cross join x cross join values 
     (0, concat('\u001B','[48;5;0m ','\u001B','[0m')),  -- Black
     (1, concat('\u001B','[48;5;15m ','\u001B','[0m')), -- White
     (2, concat('\u001B','[48;5;51m ','\u001B','[0m')), -- Light blue
     (3, concat('\u001B','[48;5;45m ','\u001B','[0m')), 
     (4, concat('\u001B','[48;5;39m ','\u001B','[0m')),
     (5, concat('\u001B','[48;5;33m ','\u001B','[0m')),
     (6, concat('\u001B','[48;5;27m ','\u001B','[0m')), 
     (7, concat('\u001B','[48;5;21m ','\u001B','[0m'))  -- Dark blue
     as palette(id, color)
where  cast(substring('012223333344445555666677770', mandelbrot(x.cR, y.cI, 27), 1) as Int) = palette.id
group by y.id 
order by y.id desc).collect()
# print out the result set of the query line by line
for line in result:
    print(line[0])
    
Explanation: Mandelbrot in SQL, displayed with color
This computes and displays the Mandelbrot set on the terminal using color, with a blue palette.
Note: it requires a terminal or notebook with support for ANSI escape codes.
End of explanation
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