Geometric Fractals

Iterated functions and space filling curves

• Fractal geometry
  • Paradoxes of the infinite, Bernard Bolzano
  • Coastline paradox, Lewis Fry Richardson
  • Fractals, fractal curves, Weierstrass function, Cantor set, Koch snowflake, Sierpiński triangle, Osgood curve, de Rham curve, Menger sponge, Lévy C curve, Fibonacci fractal
  • Karl Weierstrass, Georg Cantor , Helge von Koch, Wacław Sierpiński, William Osgood, Georges de Rham, Karl Menger, Paul Lévy
• Space filling curves
  • Recursion, scale invariance, self-similarity, lacunarity, dimension
  • Fractal dimension, Minkowski–Bouligand dimension, Hausdorff dimension
  • Peano curve, Hilbert curve, dragon curve, Sierpiński curve, Gosper curve, Z-order curve, H-tree, space-filling tree
  • Giuseppe Peano, David Hilbert, Bill Gosper
• IFS fractals
  • Affine transformations, collage theorem, iterated function system
  • Barsley fern, Michael Barnsley
  • Fractal compression
• Nonlinear fractals
  • Fractal flames, Scott Draves
  • Fractal expressionism

Discussion

• Fractals (Worls of Mathematics)
• The Case of the Missing Fractals (A. Rosenthal & G. Zaidan)
• Fractals – Hunting the Hidden Dimension
• 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

 

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