Sacred Geometry in Nature


"I am in AWE at the divine mathematics revealed in Nature . . . and that is what I seek to capture through my FRACTAL paintings based on the sacred fractal geometry of Nature." --Duncan Tooley

FRACTAL Geometry

  • Nature’s art composed from the same self-repeating shape in different sizes; the inspiration for my watercolor paintings and digitally manipulated photographs. –Duncan Tooley
  • A mathematical set that exhibits a repeating pattern displayed at every scale. It is also known as expanding symmetry or evolving symmetry.  —
  • A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. –-Google Mathematics


Natural Phenomena with Fractal Features

Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees. Phenomena known to have fractal features include:
  • River networks
  • Fault lines
  • Mountain ranges
  • Craters
  • Lightning bolts
  • Coastlines
  • Mountain goat horns
  • Trees
  • Algae
  • Geometrical optics
  • Animal coloration patterns
  • Romanesco broccoli
  • Pineapple
  • Heart rates
  • Heart sounds
  • Earthquakes
  • Snowflakes
  • Psychological subjective perception
  • Crystals
  • Blood vessels and pulmonary vessels
  • Ocean waves
  • DNA
  • Soil pores
  • Rings of Saturn
  • Proteins                                                                              –

Mathematics in Nature

“The universe is written in the language of mathematics…without which it is humanly impossible to understand a single word of it; without this language, we wander about in a dark labyrinth.”  –Galileo Galilei