Macrocosm Microcosm and Li - the fractal truth

Broccolis, brains and Mandelbrots?

Welcome to the world of fractal wonder, where macrocosm meets microcosm and Li is omnipresent in the pattern of our universe. The more you see, the more you believe. Nothing is random. The universe is mental, the universe is fractal.

what are Fibonacci Fractals?

The Romanesco broccoli is the best natural example of a Fibonacci fractal.

During the second half of the last century, Benoît Mandelbrot convinced the scientific world that Euclidean geometry, used since classical times, was actually no use to describe nature. Mountains are not pyramids, trees are not cones, coastlines are not straight. He proposed the use of a new geometry which best describes the complexity of natural forms: the fractal geometry. This could be used to describe the patterns found in nature, a system already used by the Chinese (Li) and the Egyptians for centuries (see The Emerald Tablets of Thoth's macrocosms and microcosms of the universe). 

Fractal geometry manifests itself in all aspects of the landscape. Coastlines are natural fractals and were among the first recognised.  A characteristic of fractal structures is that they are self-similar. This
means that their parts resemble the whole. Coasts are not straight lines but rather curves formed by capes and gulfs,
large protuberances that in turn are formed by bays and headlands, which in turn have their inlets and crags. Scotland and its battered coasts is a perfect coastal fractal example.


Fractal geometry is the geometry of nature. Both are based on the constant repetition of simple processes. This is so much the case that through simple logarithms based on the repetition of very minimal processes it is possible to create ‘natural’ landscapes using technology. This beautiful Norwegian coast-line shows many examples of fractals. Rivers are good examples of natural fractals, because of their tributary networks (branches off branches off branches) and their complicated winding paths.

These fractal patterns (left and below) are actually aerial photographs of unique salt marshes at Abbotts Hall Farm, near Essex, UK and an artist's detail of a brain. 

Water channels slice through the boggy ground, cutting out pathways and patterns, and some say they begin to resemble the delicate and unique surface of the human brain.

If this salt marsh was brain shaped we may take a different view point on the randomness of these patterns. Our brains are not random, or so we are led to believe. Therefore the salt marsh is not random. This leads us to conclude that a fractal is not random, and indeed this is true. Fractals are based on the Fibonacci sequence.

The Fibonacci sequence

So what does a Roman broccoli have to do with fractals and maths? The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34... Each number in this simply elegant pattern is found by adding up the two numbers before it. When you make squares with those number widths, you get a perfect spiral which we call the Golden Mean. This spiral is the key to making the broccoli beautiful. Think Spirograph in 4D.

Another of the most important qualities of fractals is that they are generated by the infinite repetition of a simple step or process. This is called iteration. It is the process or pattern that makes up the perfect broccoli. The parameters of the Romanesco broccoli are shown to be the Fibonacci sequence. Many intricate flowers and plants carry the same pattern and other systems in nature such as bees, bunnies, sunflower seeds and shell spirals. This fractal pattern present in everything is derived from an underlying principle or parameter which describes the things we see. Just like computer code it is the underlying meta data for life.

Macrocosm and microcosm - hot springs and ring nebulas

The Grand Prismatic Spring in Yellowstone National Park is the largest hot spring in the U.S. It was named for its striking colouration -  its colours match the rainbow dispersion of white light by an optical prism: red, orange, yellow, green, and blue. Without any organisms, the centre has the deep intrinsic blue colour of water, as the result of water’s absorption of red wavelengths of visible light. The edges of the pool consists of bands of different colours and each band in the “microbial rainbow” represents a mini-ecosystem.

The Ring Nebula - a massive cloud of gas around a beautiful dying star. This planetary ring nebula was photographed by NASA. The Hubble image offers the best view yet of the nebula, revealing a complex structure. The observations have allowed astronomers to construct the most precise three-dimensional model of the glowing gas shroud, called a planetary nebula. Based on the new observations, the Hubble research team suggests that the ring wraps around a blue football-shaped structure that protrudes out of opposite sides of the ring. The nebula is tilted toward Earth so that astronomers see the ring face-on.

My soul is spiraling in Frozen Fractals all around

Ice fractals spiraling 

Message in the Fractal Rose

Li is fractal & it is inside us

The Micro cosmic

A collection of the surprisingly colourful micro cosmic microcosms in our universe. Magnified images show us that coffee is made of rainbows and snowflakes are fractal jewels.

Magnified DUST is more colourful up close, pretty little village of the dust mites

No wonder it makes you giddy after a few - a kaleidoscopic vodka and tonic

This stuff makes you see kaleidoscopes - dimethyltryptamine aka DMT

Colourful coffee plant

The caffeine rainbow - a colourful start to your day

The snow flake jewel - fractal perfection

Candy of the sea - stunning SAND

What is Li?  

Li or  理 is a Chinese concept which recognizes that every thing in the universe has a dynamic form and an asymmetrical, seemingly random order. Once we look closely we see that this order is everywhere and that there is a pattern in the randomness.

Above - a Google earth fractal pattern in Li. This is an image of Spain and its many networks of rivers.

The things we see on DMT

Did you know? Broccoli fractals are found in DMT Hyperspace too.

Above and below - fractals produced using the Fibonacci sequence - the Mandelbrot Set. Also spotted in Hyperspace.

The Donana Marshes

Brain tree or a tree brain? 

The salt marshes of southern Spain’s Coto Doñana National Park seem alive, breathing, organic and brain-like, with capillaries or branches, caused by the "branches off branches off branches" effect that the tributary 

network of complicated paths create.

Above - tree of life?

These stunning images were taken by photographer Héctor Garrido and feature in his book Doñana and the Marshes. 

Below - Brain or salt marsh?

Macro fractal 

These beautiful macro shots of water droplets show the luscious Li patterns full of fractal goodness. By Heinz Maier.

More Fractal Goodness yum

Coral colours the coastal rocks like brains splattered by the waves. 

The crackle effect on dry mud also has a shattered egg shell feel to it.

Feathery fern fractal frolics.

Lava and cracked rock help form fractals over the ages...

...then rock, sand and water combine to make ancient fractal art.

Perfect plant spiraling fractals.

Simple but stunning leaf fractal.

Ripples in the wind and the waves create the shape of invisible fractals.

Pockets of ripples more fractals in nature.