Fractal Geometry and Frame Design
Mon, January 6, 2020 
Benoit MandelbrotFractal is a word coined by mathematician Benoit Mandelbrot (Left.) who published his findings as recent as the 1970s.
Up until that point, throughout history geometry was all about straight lines, triangles, pyramids, circles and cylinders, etc.
This geometry applied to everything man-made, buildings, bridges and other engineering projects, and of course bicycle frames fit right into this category, being made up of straight lines and triangles. Up until Mandelbrot’s findings, everything in nature outside of that which is man-made could not be explained by geometry and mathematics.
Mandelbrot changed all that when he discovered that shapes and forms in nature. For example, cloud formations, trees, mountains, river flow and even blood vessels in our bodies, were a series of repeating irregular shapes, which could be recreated and proven mathematically.
Like many great minds, Benoit Mandelbrot was at first scoffed at by other experts, but now with improvements in computing his theories are being proved mathematically. Now taken seriously, fractals are being studied and used in the medical and the environmental fields.
One of the places we also see fractal geometry in practice is in special effects for movies. Not only are images of nature being created, like landscapes, plants, trees, and even human and animal forms, but fire and explosions can be created and animated on a computer.
This subject has always fascinated me, because on the one hand you have the bicycle which is traditional man-made geometry, and the task of the frame builder is to match that to the human body, so the two become one, and the bicycle becomes an extension of its rider.
The human body, like all forms in nature, appears to be chaotic and infinite in its makeup. Yet it was possible for me to build a series of production frames, the Fuso for example, in a range of sizes that would fit just about anybody.
From as far back as the late 1960s I found I could fit someone to a frame “Intuitively.” I did not let this be widely known for fear of being labeled a crack-pot. I was basing my estimation of frame size primarily on a person’s height.
Long after I left the bike business, and therefore the effect of the “Crackpot” label had diminished, I wrote an article here in February 2006, stating that frame size could be estimated around a person’s height.
I came to this conclusion, not so much by what I could do in sizing a person, but more by what I could not do. A person who is six feet tall would normally fit on a frame around 58 or 59 centimeters (Measured center to top.)
However, it is quite a common occurrence to find a person six feet tall (183 cm.) with a 30 inch (76 cm.) inside leg measurement. You cannot put a person like that on a 51 centimeter frame as his inseam would suggest then build a long top tube to accommodate his long body.
I would simply drop the frame size down to a 56 or 57 centimeter because of the short legs, and leave the top tube as standard for that size frame. (55cm. or 55.5 respectively.) This same frame would also suit a person 5’10” tall, (178 cm.) with an inseam around 33 inches.(84 cm.) The difference being the taller guy with short legs would have his saddle lower and possibly use a longer stem.
I knew this was so, but never knew why. It all became clear to me on watching a PBS Nova episode back in 2010 on Benoit Mandelbroc and his discovery fractal geometry. The program mentioned a group of environmentalists were studying rainforests. They cut down a large tree, then measured and documented the dimensions of all its branches, overall height etc.
They then found that a seemingly random pattern of trees of all sizes growing throughout the rest of the rainforest followed the same pattern as the branches of the one tree they had documented; both in the position of their branches, and their position in the forest relative to other trees.
Watching this, it occurred to me that if you took a large group of humans all the same height, you could fit them all to the same size bicycle frame. (Within a centimeter or so.) This is why this theory works, although on the surface it appears that my group all the same height are each different in every other way, they are no different than the trees in the rainforest. They all follow the rule of fractal geometry that can be plotted mathematically.
Fractals are once again in the news with this recent article, which prompted me to re-visit my previous piece written back in December 2010.
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Reader Comments (2)
Thnaks Dave. Interesting post. I learned something.
Here is Wolfram's note on Mandelbrot:
https://blog.wolfram.com/2010/10/21/benoit-mandelbrot/
Thanks Dave !