Minecraft wiki entry for Taxicab_distance, associated text: Light from light sources such as torches, campfires, lanterns, glowstone, etc. illuminate surfaces according to taxicab distance.
Torches also also melt snow layers within 2 blocks and ice within 3 blocks taxicab distance.
Heat blocks‌[Education Edition only] melt snow layers and ice within 2 blocks taxicab distance, but do not emit light.
Liquid (water or lava) flowing horizontally on a flat surface flows from the source in taxicab distance. For example, if flowing water is forced into a 1-block-wide stream and turns corners, it travels 7 blocks. If it is allowed to flow freely on a surface, it also travels 7 blocks taxicab distance.
In Bedrock Edition, simulation distance is the distance from the player at which blocks get tick updates (such as lightning strikes), and beyond which mobs despawn; this also uses taxicab distance.
In Bedrock Edition, a spawner spawns mobs within a 4-block taxicab horizontal range from the spawner.
A sponge absorbs water up to 7 blocks away in taxicab distance (an octahedral volume centered on the sponge).
Phantoms in Java Edition spawn 20–34 blocks above the player, and off to the side by a taxicab distance of up to 10 blocks.
Using bone meal on sea pickles that are on coral blocks creates more sea pickles on nearby coral blocks out to a horizontal taxicab distance of 2.
A block of copper is oxidized according to a taxicab distance search for unwaxed copper blocks within 4 blocks of the block being considered for oxidation.
Shulkers can move along only one of the three grid axes at a time and on integer steps, meaning that they move according to taxicab geometry.
Some redstone components produce block updates up to two blocks away by taxicab distance, including up and down.