Esthetics & Design: Fractals

esthetics - fractalsHand-out for a workshop on Esthetics & Design in Permaculture.

Patterns in Nature: self-similarity & scale 

  • Exact self-similarity: identical at all scales; e.g. Koch snowflake
  • Quasi self-similarity: approximates the same pattern at different scales; may contain small copies of the entire fractal in distorted and degenerate forms
  • Statistical self-similarity: repeats a pattern stochastically so numerical or statistical measures are preserved across scales
  • Qualitative self-similarity: as in a time series

Multifractal scaling: characterized by more than one fractal dimension or scaling rule.