Fractals
Infinitely complex patterns generated via recursion that are self-similar across all scales. Thought to be found in abundance in nature, though "true" (infinite) fractals are not possible because nature uses physical matter, which has particular structures at the microscopic and smaller scales (molecules, atoms, elementary particles, etc).
Fractal features can be observed in nature in tree branching structures, leaf veins, terrain, surface textures, coastlines, rivers, succulents, snowflakes, rivers, lightning bolts, nautilus shells (both form and pattern), and so much more.
Key terms:
- Fractal dimension - ratio providing a statistical index of complexity comparing how detail in a fractal changes with scale.
- Self-similarity - when something is exactly or approximately similar to a part of itself.
Notable fractals:
- Apollonian gasket (a.k.a. curvilinear Sierpiński gasket)
- Barnsley fern
- Cantor set
- Chaos game
- Dragon curve
- Hilbert curve
- Iterated function systems (IFS)
- Julia set
- Koch snowflake
- Menger sponge
- Mandelbrot set (related: Mandelbulb and Buddhabrot)
- Sierpiński triangle / gasket / sieve and carpet
- ... and so much more
Articles:
- Fractal on Wikipedia
- List of fractals by Hausdorff dimension on Wikipedia
- Fractals, Caos, Self-Similarity by Paul Bourke
- Chapter 8. Fractals in Daniel Shiffman's Nature of Code book
- Fractals by Paul Bourke Notable software:
- glChAoS.P by Michele Morrone (BrutPitt)