what is Mandelbrot set ?
In: Mathematics
Say you have a tabletop. You pick any spot on the table and you measure how far over your spot is (left to right) and how far up (bottom to top). That gives you two numbers. You “do a math” on these two numbers and that gives you two new numbers, and you can measure to find out where you are now on the tabletop. Then you “turn the crank” by doing the math thing again on the new spot, and so on, to get your next spot, and again, and again.
Depending on where your starting spot is, as you keep “turning the crank”, your sequence of next spots might:
* Quickly end up off the table
* Bounce around somewhat but stay on the table
Most of the time, if you pick two starting spots that are very close to each other, as you “turn the crank” each starting spot leads to a very similar sequence of next spots. But the cool part is that there are some places where even a tiny change in where you place your spot can have a huge change in where you end up. We call those parts “chaotic”.
If you color each spot based on how many times you can turn the crank before the answer flies off the table, you get extremely beautiful color patterns and curls and wiggles around the chaotic parts. And if you could somehow zoom in, it would never get smooth, you would keep seeing ever tinier curls, forever.
And all this beauty comes from some fairly simple looking math (not simple to a 5 year old, but lots of 12 year olds can grasp it).
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