FRACTALS AND CONNECTION TO LUNGS

Fractals and connection to lungs

INTRODUCTION:

A fractal is a never ending pattern that repeats itself at different scales.

This property is called “Self-Similarity.”

Fractals are extremely complex, sometimes infinitely complex - meaning you can zoom in and find the same shapes forever.

Amazingly, fractals are extremely simple to make.

A fractal is made by repeating a simple process again and again.

NATURAL FRACTALS

BRANCHING

Fractals are found all over nature, spanning a huge range of scales. We find the same patterns again and again, from the tiny branching of our blood vessels and neurons to the branching of trees, lightning bolts, and river networks. Regardless of scale, these patterns are all formed by repeating a simple branching process.

A fractal is a picture that tells the story of the process that created it.

Neurons from the human cortex. The branching of our brain cells creates the incredibly complex network that is responsible for all we perceive, imagine, remember. Scale = 100 microns = 10-4 m

Our lungs are branching fractals with a sur­face area ~100 m2. The similarity to a tree is significant, as lungs and trees both use their large surface areas to exchange oxygen and CO2. Scale = 30 cm = 3*10-1 m.

Lichtenberg “lightning”, formed by rapidly discharging electrons in lucite. Scale = 10 cm = 10-1 m.

Oak tree, formed by a sprout branching, and then each of the branches branching again, etc.

Scale = 30 m = 3*101 m.

River network in China, formed by erosion from repeated rainfall flowing downhill for millions of years.

Scale = 300 km = 3*105 m.

NATURAL FRACTALS

SPIRALS

The spiral is another extremely common fractal in nature, found over a huge range of scales. Biological spirals are found in the plant and animal king­doms, and non-living spirals are found in the turbulent swirling of fluids and in the pattern of star formation in galaxies.

All fractals are formed by simple repetition, and combining expansion and rotation is enough to generate the ubiquitous spiral.

A fossilized ammonite from 300 million years ago. A simple, primitive organism, it built its spiral shell by adding pieces that grow and twist at a constant rate. Scale = 1 m.

A hurricane is a self-organizing spiral in the atmosphere, driven by the evaporation and condensation of sea water. Scale = 500 km = 5*105 m.

A spiral galaxy is the largest natural spiral comprising hundreds of billions of stars. Scale = 100,000 ly = ~1020 m.

The plant kingdom is full of spirals. An agave cactus forms its spiral by growing new pieces rotated by a fixed angle. Many other plants form spirals in this way, including sunflowers, pinecones, etc. Scale = 50 cm = 5*10-1 m.

The turbulent motion of fluids creates spirals in systems ranging from a soap film to the oceans, atmosphere and the surface of jupiter. Scale = 5 mm = 5*10-3 m.

A fiddlehead fern is a self-similar plant that forms as a spiral of spirals of spirals.Scale = 5 cm = 5*10-2 m.

GEOMETRIC FRACTALS

Purely geometric fractals can be made by repeating a simple ...