I look for simple explanations online and I don’t understand.
In: Mathematics
The mandelbrot fractal appears when you try to plot the answer to a specific infinite series.
Take any complex number Z0 (wich has a real part X and an imaginary part Y so Z=X+iY with i×i=-1)
Then repeat this calculation:
Z_(n+1)=(Z_n)²+Z0
So basically every step you square the number and then add the number you started with.
Repeat this infinite times, and depending on what starting number you picked you either get a finite (it converges) or infinite (it diverges) value.
Usually you then colour the starting point in black for converge, or in a colour thats brighter the faster it diverges.
The mandelbrot fractal shows that the question if a certain starting value diverges or not is extremely hard to answer. There are infinitely complex areas, where no matter how far you zoom in you will find more details. (And therefore changing the input value 100 digits after the decimal point *can* radically change the output in unpredictable ways)
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