morkev/math-visualization

A compilation of mathematical visualizations – fractals, bifurcations, curves, etc.

Logistic Map

Generates a bifurcation diagram of the logistic map. We can obtain this by plotting as a function of r, a series of values for x_n obtained by starting with a random value x₀, iterating many times, and throwing away the initial points, which correspond to values before the iterations reach the attractor.

In other words, the set of fixed points of x_n corresponding to a given value of r are plotted for increasing values of r.

Expected output

Peano-Gosper Curve

The Gosper island can be duplicated seven times and linked to create a shape that is comparable to it in all dimensions but scaled up by a factor of √7.

A tessellation of the plane results from endlessly repeating this technique. The curve itself can also be expanded to encompass the entire plane with an infinite curve.

Fractal dimension:

$D= \frac{2\ In\ 3} {In\ 7} = 1.129...$

Effective hierarchical hexagonal clustering and indexing can also be achieved using the Gosper curve.