fractalview

Prototyped with CodeSandbox

To run:

npm install
npm start

you can also play around with this in codesandbox here: https://codesandbox.io/p/github/bryanjj/fractalview/

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This app visualizes the 4d space of mandelbrot and julia sets. this space is a $f: \mathbb{C}^2 \to \mathbb{C}$ space defined with the function: $Z_{n+1} = Z_{n}^2 + c$ for which the boundary of the points $Z_0$ and $c$ converges

this is a 2d-complex space and the app views a 2d-real slice of this space.

You configure the 2d slice you are viewing by mapping the 4 real dims to the 2 dims (x and y) of the view window

the other dims not assigned to x and y can be set to specified constants. This allows you to view the 4d space from any orthogonal slice.

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The mandelbrot set is defined as: the set of points c, where the following recursive function converges $Z_{n+1}=Z_{n}^2$ + c$ where $Z_0 = 0$

So to configure the classic mandelbrot set you would set the following coord mappings:

real $Z_0 = 0$

imag $Z_0 = 0$

real $c = x$

imag $c = y$

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The julia sets are defined: as the set of points Z0, where the following converges: $Z_{n+1}=Z_{n}^2 + c$ where $c$ is a constant

for example:

real $Z_0 = x$

imag $Z_0 = y$

real $c = -.4$

imag $c = .6$