Fractal Lab
Fractals, all the way down.
An interactive reference for complex dynamics, geometric, IFS, L-systems, and dimension theory. Explore. Zoom. Measure.
Fractal families covered
Every family gets its own catalog page with definition, construction, dimension, applications, and references.
Complex dynamics
Mandelbrot, Julia, Newton, Burning Ship, Multibrot. Escape-time iterations over the complex plane.
Geometric
Cantor set, Koch snowflake, Sierpinski triangle, Menger sponge, Dragon curve. Self-similar constructions.
Iterated function systems
Barnsley fern, Sierpinski via IFS, chaos game, fractal flames. Affine contractions iterated.
L-systems
Lindenmayer rewriting rules, turtle graphics. Plants, dragons, Koch curves via grammar.
Dimension & measure
Hausdorff, box-counting, correlation, Lyapunov dimension. What 'fractal dimension' really means.
What is here today
Mandelbrot explorer
Pan, click-to-zoom, iteration-count slider. The whole boundary in your browser at interactive speed.
Fractal catalog
Mandelbrot, Julia, Sierpinski, Koch, Cantor, Dragon, Menger, Newton. Each with definition, dimension, where it shows up, references.
FAQ
What is a fractal, what does fractal dimension mean, why does the Mandelbrot boundary have dimension 2, and similar.
References
Bibliography of canonical books and papers: Mandelbrot, Falconer, Barnsley, Peitgen and Saupe, Devaney, more.
IFS designer
Build your own iterated function system: add/remove affine maps, drag sliders, check contractions, estimate dimension, export JSON.
L-system editor
Write your own axiom, rewrite rules, and turtle parameters, including stochastic rules and branching, and watch the curve render in real time.
Escape-time designer
Pick an iteration family (polynomial, perturbed, burning-ship, sin, exp), tune exponents, switch Mandelbrot/Julia. Click to zoom.