The Remarkable Story Behind the Mandelbrot Monk

April 02 2009 Samir Khan 519

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While visiting a cathedral in Germany, Bob Schipke, a retired Harvard mathematician was astounded to find a glyph in a 13th century manuscript that looked remarkably like the Mandelbrot set.  This led to a remarkable voyage of discovery that was publicised in a 2001 article by Ray Girvan, the noted British science writer.

An excerpt from the Codex Udolphus.  Note the fractal on the top right-hand corner

Schipke was so fascinated by the discovery that he enlisted the help of a historian at the University of Munich and researched the author of the manuscript – a monk called Udo of Aachen.  He found a Latin treatise called the Codex Udolphus. 

According to the treatise, Girvan notes that

... Udo's aim was to devise a method for determining who would reach heaven. He assumed each person's soul was composed of independent parts he called "profanus" (profane) and "animi" (spiritual), and represented these parts by a pair of numbers. Then he devised rules for drawing and manipulating these number pairs. In effect, he devised the rules for complex arithmetic, the spiritual and profane parts corresponding to the real and imaginary numbers of modern mathematics.

In Salus, Udo describes how he used these numbers: "Each person's soul undergoes trials through each of the threescore years and ten of allotted life, encomassing its own nature and diminished or elevated in stature by others [it] encounters, wavering between good and evil until [it is] either cast into outer darkness or drawn forever to God."

When Schipke saw the translation, at once he saw it for what it was: an allegorical description of the iterative process for calculating the Mandelbrot. In mathematical terms, Udo's system was to start with a complex number z, then iterate it up to 70 times by the rule z -> z*z + c, until z either diverged or was caught in an orbit.”

Anyone who wants to learn more about Udo of Aachen must read Ray Girvan’s remarkable article at http://apothdrawer.blogspot.com/1999/04/mandelbrot-monk.html.

P.S.  If you’ve got this far and believe the story, then April Fool! There are several internal clues in Ray Girvan’s original story that reveal it as a clever joke – how many can you spot?

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