Why do we need to use complex numbers to generate fractals?

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Brownpanda

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I understand that complex numbers are used to generate fractals such that the normal number represents the x-axis and the imaginary number represents the y-axis. Why not use normal algebraic x,y equations instead?
 
Who said you can't? Who said you need to use complex numbers?

It's just that complex numbers provide one natural way to produce certain kinds of fractals. Look up fractals, and you'll find very different kinds.

And obviously where a fractal was discovered using complex numbers, you can rewrite the equations involved using the components (real numbers) instead. That just makes it more complicated.
 
You don't "need to" but one-dimensional fractals are not very interesting. And points in the two dimensional plane, (x, y), can be most easily handled as single complex numbers, x+ iy.
 
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