Julia fractal

This is an interactive playground where you can try out how the fractal changes with respect to a hyper parameter c.

Points represent initial parameters to a function \(f_c(z) = {z^2 + c}\) where values quickly explode to infinity after iteration.
Those are called unstable points.

Example path is visualized from point A as initial input to function above.
Path represents the steps after each iteration.

If you move point A to a dotted zone, you will see that the path doesn't converge to the center (point x=0, y=0), but instead goes to infinity.

Also try moving point C to change the hyper parameter and see how the fractal changes.

More about fractals from Numberphile.