Geometric Fractals

Iterated functions and space filling curves

• Fractal geometry
  • From the history of curves
  • Transformations & iterations
  • Mathematical monsters & maverick mathematicians
• Space filling curves
  • Hausdorff and Minkowski dimensions
  • Complexity and self-similarity
• Iterated function systems
  • Affine transformations
  • Collage theorem
  • Fractal compression
• Fractal flames
  • Nonlinear transformations

Resources

• Fractals (Worls of Mathematics)
• The Case of the Missing Fractals (A. Rosenthal & G. Zaidan)
• Fractals – Hunting the Hidden Dimension
• The Science and Art of Fractal Geometry
• Fractal Geometry (Michael Frame, Benoit Mandelbrot & Nial Neger)
• Classic Iterated Function Systems (Larry Riddle)
• Design Fractal Art: An Introduction to Apophysis (Stan Ragets)

Assignment

Fractal flames

Apophysis (with mods) – Brazil Design – DesignIFS – Dragon – Electric Sheep – Flam4 – Fractal Machine – Fractaline – Fractron9000 – IFS CAD – IFS Construction Kit – IFS Fractal Editor – IFS Generator – JWildfire – Oxidizer – QSFlame – SpaceFillingCurves – TeraFractal – Wonderland

Gallery of fractal flames  »