Fractal Lab

Interactive Fractals Explorer in Magenta-Galaxy style.

Fractal Lab is my playground for the fractals I really like. I remember the first time I saw the Mandelbrot Set in school and I asked my teacher "What is the point of this?". He replied "It just shows the beauty of Mathematics, Ivelina.".

There are many different types of fractals from complex dynamics, recursive geometry, stochastic ideas, and iterated systems and so on. I am trying to build a full list of them here.

Complex Dynamics

Mandelbrot Set

Canonical escape-time fractal generated by iterating $z_{n+1}=z_n^2+c$ with $z_0=0$.

Wikipedia: Mandelbrot Set

220

Julia Set

Julia families for fixed complex parameter $c=\operatorname{Re}(c)+i\operatorname{Im}(c)$.

Wikipedia: Julia Set

-0.79 0.15

Tip: wheel to zoom, drag to pan.

Recursive Geometry

Koch Snowflake

A recursive boundary construction where each segment is replaced by a four-segment motif.

Wikipedia: Koch Snowflake

4

Dragon Curve (Heighway Dragon)

A recursive self-similar curve generated by repeated folding and turn rules, producing a striking geometric ribbon.

Wikipedia: Dragon Curve

11

Hilbert Curve

A space-filling curve built recursively, showing how a one-dimensional path can increasingly fill a two-dimensional region.

Wikipedia: Hilbert Curve

5

Iterated Function Systems

Barnsley Fern

An iterated affine system that generates a fern-like attractor from simple probabilistic transforms.

Wikipedia: Barnsley Fern

50000 1.00

Stochastic Fractals

Brownian Motion

A stochastic path visualisation showing random trajectories with softly glowing, galaxy-math styling.

1200 1.7