Friday, December 3, 2010

Father of Fractals

You may have already heard the recent news of the passing of Benoit Mandelbrot, originator of the iconic Mandelbrot Set (pictured) and founder of the field of fractal geometry.  It brings to mind the deeper understanding of human structure and function that has resulted directly from applying principles of fractal geometry.  An important set of principles that I believe we A&P professors could do a better job of helping our students appreciate.

Mandelbrot's pioneering efforts in understanding the roughness of nature led to the discovery of basic principles of fractal geometry.  A key characteristic of fractal structures is self-similarity (the parts resemble the whole).

In human anatomy, this self-similar characteristic is observed in surfaces that have folds, which have bumps, which in turn have their own bumps, and so on . . . producing unexpectedly huge total surface areas.  For example, think of the loops of the intestines, which in turn have circular folds of mucosa, which in turn have villi, which in turn have microvilli, which in turn have membranes embedded with bumpy molecules, and so on. 

Fractal self-similarity can also be observed in branched structures, such as the respiratory tract and the cardiovascular vessels.  These structures have branches that have branches that have branches, and so on for many levels . . . producing large numbers of pathways and huge surface areas.

A particularly interesting characteristic of such complex fractal structures is that they are produced with relatively simple mathematical formulae.  Which means that very little genetic information is needed to produce highly complex structures like intestines, blood vessels, lymphatic vessels, bronchial trees, cerebral convolutions, etc.

Fractal structures are also chaotic, a mathematical concept of "constrained randomness."  Put simply, chaotic structures have an element of randomness but within limits.  So when our body applies fractal geometry during development we can be certain of a particular type of structure without being certain we'll know exactly where each individual bump or branch will lie.  In other words, we can more or less be certain where the main arteries will be (with some individual variation) but not so much for the various arterioles and capillaries . . . at least not precisely.

Principles of chaos also play out in human physiology when we observe the aperiodic (nonrhythmic) patterns of heart rate, brain waves (as in an EEG), and certain other functions.

Mandelbrot opened up a whole new understanding of human structure and function that is only now becoming understood widely.  I've been introducing the concept of chaos and fractals in my courses, and more subtly in some of my textbooks, for several years now.  My experience is that introducing simplified principles of chaos and fractals at the beginning of A&P 1, then reinforcing them when encountered throughout both semesters of A&P, help student appreciate an intriguing and important concept of human structure and function.  A concept that is increasingly playing a central role in science's understanding of human biology.


Want to know more?

Benoît Mandelbrot (1924–2010)
Ralph Gomory
Nature Volume: 468, Page 378, Date published: 18 November 2010, doi:10.1038/468378a, Published online: 17 November 2010
[A brief synopsis of Mandelbrot's life and contributions from the journal Nature]

Chaos in the Human Body (Mini Lesson)
Kevin Patton
Lion Den http://lionden.com/chaos.htm
[Brief outline that I use with my own students in A&P 1]

Applications of Fractals - Human Body
ThinkQuest
Oracle Education Foundation. online (accessed 2 Dec 2010)
[Brief student-produced outline of some fractal principles of the body]

Fractal Geometry in Biological Systems: An Analytical Approach
Philip M. Iannaccone, Mustafa Khokha
CRC Press 1996
[Book outlining the initial discoveries of fractals in humans.]

Chaos: Making a New Science
James Gleick
Penguin 2008
[Reprint of the classic bestseller book that outlines in simple terms the concepts of chaos and fractal geometry.  Highly recommended.  Includes some applications/examples in human biology.]

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