I look for simple explanations online and I don’t understand.
In: Mathematics
Its an apparently simple mathematical process. You take a number and square it, then square it again and so on. One of two things will happen. It will get very very large 2, 4, 16, 256, … or it will get small 1/2, 1/4, 1/16 …. depending if your start point is above or below 1. Easy enough for real numbers.
However if you do the same for “complex” numbers, things get complicated. Complex numbers involve “i”, the square root of -1 so look like (x + y*i) and can be represented on a flat plane with x and y axes instead of a line like “real” numbers. The Mandlebrot set is the border between the start points on the plane that stay small and those that cross the border and grow uncontrollably.
Its really the black area in the middle, numbers that stay small after an infinite number of squarings, but obviously you can’t do that. So you calculate it a specific number of times and colour the points that cross the border before that time with one colour, the group that are still OK after the next set of calculations with another colour and so on. You build up a contour map of how long each start point survives before growing.
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