Due to the nature of fractals, their edges are infinite in length, because you can always add another iteration.
Raised fractal patterns on the shoe would provide very good grip, due the infinite number of tiny gripping edges.
It would also leave very interesting footprints.-- DesertFox, Dec 09 2005 Shoes For Crews - Safety Shoes http://ShoesForCrews.Com/[Walabio]'s linky, cut'n pasted for your delectation [Dub, Jul 28 2009] Awesome.-- migennes, Dec 09 2005 and when you took them off would this be called "a fractical shoe loosen "? +-- xenzag, Dec 09 2005 A pair of Mandelbrot brothel creepers for me.-- wagster, Dec 09 2005 Nice idea - but how long does it take to make the mould for the treads?-- Dub, Dec 09 2005 Love the idea, but [Dub]'s question is priceless. If only I could get my own engineers to think about design for manufacture...-- normzone, Dec 09 2005 Gissa-job!-- Dub, Dec 09 2005 "very good grip" - actually, per the gecko's foot, I think you'd have a hard time lifting your feet at all, as it would bond to the floor.-- DrCurry, Dec 09 2005 Good good stuff, [Dfox]. I wonder if an enormous fractal could be stamped in a huge rubber sheet, then soles cut from this. No two soles would be alike, though all would be similar. If there was someway to generate the fractal directly on the rubber (perhaps diffusing oil on the rubber, or a growing crystal) that would be a magnitude cooler.-- bungston, Dec 09 2005 would the gluey thing get less as it all got smaller?
+1-- po, Dec 09 2005 K, Q, and X?
Edit: Ahh, Idea title starting letters, I have every letter but K, Q, and X. Aha!-- DesertFox, Dec 09 2005 Big fractal, bounding through the snow!
"what can this foot print mean?" +-- skinflaps, Dec 09 2005 'Twas the Yetibrot!"-- wagster, Dec 09 2005 The shoe print of God.-- 2 fries shy of a happy meal, Dec 10 2005 Hah!-- DesertFox, Dec 10 2005 Not to be a spoilsport, but wouldn't the finer iterations wear away in minutes, leaving less and less fracticality every day?-- GutPunchLullabies, Dec 10 2005 it takes quite a bit of time to wear through an infinite tread.-- daseva, Dec 10 2005 A shoe print so unique, you could NOTARISE whatever you stepped on.
Swank. [+]-- Letsbuildafort, Dec 10 2005 Mandelbrot, the new Paisley for the trendy mathematician.
I've always wondered why fractals were said to be infinite in edge length. Has anyone proven that they don't converge to some finite number?-- RayfordSteele, Dec 11 2005 Would the infinite edge be infintely hard to clean when you stepped in finite doggy-doo?-- energy guy, Dec 11 2005 Just spray it with an infinite amount of water!-- DesertFox, Dec 11 2005 Wouldn't the "infinite length" in this case be analagous to an infinite geometric sequence, in that it does converge to a number, but never actually reaches it?-- Cuit_au_Four, Dec 12 2005 Depending on which type of fractal you use, the change in edge-length varies. A good example is the sawtooth fractal, which doubles ever iteration.
Ahhh, remember Pratchett on 7-league boots, and their proper use?-- DesertFox, Dec 12 2005 I can see this working down several levels of fractility, but after about ten levels, wouldn't the texture of the rubber soles exceed the fractal pattern? +-- Sparty, Dec 12 2005 Thank you, Sparty. Well asked.-- baconbrain, Dec 12 2005 It would of course. Fractals are only infinite in length conceptually and mathematically. As soon as you introduce them to the real world all that infinite stuff gets ignored by atoms and the like.-- wagster, Dec 12 2005 A friend once claimed that the M25 is a fractal, for although it encloses a finite area (Greater London), it takes a near infinite amount of time to traverse, and must therefore be infinitely long.-- coprocephalous, Dec 12 2005 If you can create an infinite series in reality, please let me know.-- Antegrity, Dec 12 2005 I stumbled upon this yesterday. I am 4 years late, but I have some feedback:
At the time this idea appeared, Shoes For Crews:
http://ShoesForCrews.Com/
Already had fractal treads. Shoes For Crews gloats that these shoetreads reduces claims for slip-injuries in Workers’ Compensation by over half.
The good news is that fractal treads work. The bad news is that someone else already patented it. The good news is that the patent only covers a specific fractal pattern and that one can create and patent a new fractal pattern for tire/shoe-treads.-- Walabio, Jul 26 2009 [Walabio]'s linky-- Dub, Jul 28 2009 Those shoes don't have fractal soles, nor do they remotely resemble fractals in any way, which leads me to believe that new user [Walabio] is just advertising for that company and should have his/her comments removed – post-haste!-- theleopard, Jul 28 2009 The soles seem to have largish squares each divided into four smaller squares, which hints at fractalness, kind of.-- spidermother, Jul 28 2009 doubtful that a company shill would use the phrase "the company gloats that..." in a spam post. The word "fractal" doesn't appear on their website anywhere.-- FlyingToaster, Jul 28 2009 Intelligent spammification perhappenstance?-- theleopard, Jul 28 2009 I like the idea but you'd have to make it from something that wouldn't lose its fractility within 50 yards of walking from abrasion.-- FlyingToaster, Jul 28 2009 ¡I am not a spammer! I just stumbled upon this site and noted that fractal soles already exists. Indeed I wear them. I work in a restaurant. The claims about slipresistance is on the website:
http://tinyurl.com/m9tj6w
If one looks at the pattern it is an obvious fractal. It is selfsimilar on multiple scales.
It is true that the site never uses. The word fractal. I see 2 reasons it might not state that the design is fractal:
It is a tradesecret.
Perhaps a genetic algorithm created the pattern and the company does not realize that it is a fractal.
I suspect the former because the company calls it SFC Mighty Grip. SFC is an acronym for Space-Filling Curve. Space-filling curves are a subset of fractals and the pattern on the sole is a space-filling fractal curve:
http://tinyurl.com/nywguf
This all seems to boil down to confusing about what a fractal is:
http://tinyurl.com/nofo5q
Many people are under the impression that fractals are always chaotic. Many fractals are totally regular like the Sierpiński- Triangle
http://tinyurl.com/m9gqvd
The only requirement for fractals is selfsimilarity.
The point is that for years, I wore shoes with fractal treads as have millions.
Ever since I stumbled upon this page and decided to chimein, /i thought about fractal treads and came up with mine own:
Start off with a right-angled isosceles triangles. The the groove between the hypotenuse is 1 millimeter wide, 1 centimeter deep and 1 decimeter long. The groove between the legs is the squareroote of the hypotenuse in width, length. and depth. Start cutting then in half with grooves the squareroot of the legs. Iterate until the one makes hypotenuses less than 1 millimeter long. This should be near the limits of what one can do with a mold. One should get great traction with that space- filling fractal curve.-- Walabio, Jul 29 2009 random, halfbakery