what is Mandelbrot set ?
In: Mathematics
In an orderly system a small change in input causes a small change in output. If you only nudge the gas, your car only accelerates a tiny bit. If you throw your next ball a tiny bit harder it will only go a tiny bit further than the last.
In a chaotic system a tiny change can cause a categorically different outcome. A little nudge can save your pinball and change the outcome of the game entirely. The path of a storm can change based on the turbulence from a butterfly’s wings.
If you map the input zones for different outcomes in an orderly system, the boundaries are simple lines. Think of a [phase diagram for water.](https://i.redd.it/yes94d114ki61.png) There’s an easy, predictable relationship between the temperatures and pressures where ice changes to liquid water.
The Mandelbrot set is the chaotic version of this map. Since tiny changes can have big outcomes, the border between one phase and the other is jagged, and it stays jagged no matter how far you zoom in.
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