Fractals exist everywhere in nature, creating infinite, mind-bending patterns that are even stranger than a casual glance may show. Indeed, even their definition causes disagreements between scientists and researchers.
A fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension.
Mandelbrot described a fractal as:
“a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole”
We love that these complex shapes can be found in nature, foods (romanesco, anyone?) and also deep within the brain, when on a psychedelic experience.
Regardless of how you define it, the scientific and visual nature of fractals make them fascinating to explore. And isn’t expanding the mind a good thing?
The images here are computer generated, built by feeding a simple equation its own output millions of times and coloring each point by how quickly it runs away to infinity. That is the whole trick of the Mandelbrot set, first plotted in 1980, and of the swirling Julia sets that grew out of it. Zoom in on any edge and the same spirals and seahorse tails reappear at every scale, which is what mathematicians mean by self-similarity. Nature arrives at the same forms by a different route. A fern leaf, a lightning bolt, a river delta, the branching of your own lungs, and the spiral florets of romanesco broccoli all repeat their own structure at smaller and smaller sizes, because growth by simple repeated rules is the cheapest way to fill space.
If patterns like these pull you in, we have collected a few relatives. Snowflakes grow their six-fold branches by the same repeated rules, micro worlds under a laser scanning microscope reveal the geometry hiding in ordinary things, and these sand designs are the meditative, hand-drawn version. Our glossary of visual culture covers the vocabulary of pattern and form.
1 Comment
There’s a fun/cool app Frax you probably know it…it’s a little phone fun…these are very cool 😎 smiles Hedy