Fractal Foundation Online Course - Chapter 1

Fractal Neurons

Our brains are full of fractals! In fact, they couldn't function if not for fractal geometry. The human brain comprises approximately 100 billion neurons. Amazingly, there are about 100 trillion synapses, or connections, among these brain cells. That's an average of 1000 connections for a given cell, though some neurons may only make a single connection, while others may have hundreds of thousands of synapses with cells all over the brain. The axons reach out to make synaptic connections with the dendrites of other neurons. It is the fractal branching pattern of the neuron's axons and dendrites that allows them to communicate with so many other cells. If neurons were shaped like cubes and neatly packed into the brain, one neuron could only connect with at most 6 other cells.

Hippocampal neurons. Scale approximately 700 microns. Image courtesy of Paul de Koninck, Universite Laval.

Hippocampal neurons (green) and glial cells (red). Scale approximately 90 microns.
Image courtesy of Paul de Koninck, Universite Laval.

The entire human brain has a volume of approximately 1500 cm³. The cortex is a thin, convoluted layer on the outside surface of the brain. An anatomical study found that the average (mean) cortical area in humans was 320 cm² with a mean thickness of 2.2 mm, giving a cortical volume of approximately 70 cm³. ^REF
Another study claims there may be 3000 meters of axons per mm³ of cortical tissue.^REF

Human brain showing the convoluted cortex.
Image courtesy of Wikimedia Commons.

According to these values, how many kilometers of axons are there in the entire cortex? [ ]

In Chapter 5, Chaos, we will explore with a simulator the firing patterns of individual neurons which themselves can behave chaotically.