A connection between the Mandelbrot set and the way nature operates...
April 3, 2014 1:39 AM Subscribe
Arthur C. Clarke, Benoit Mandelbrot, Stephen Hawking, David Gilmour and many more trip the fuck out about Fractals, the Colors of Infinity.
This is an astonishing 'deep dive' into the set. It's a long journey, and your eyesight will be wobby at the end, but wow.
posted by panaceanot at 3:37 AM on April 3, 2014 [7 favorites]
posted by panaceanot at 3:37 AM on April 3, 2014 [7 favorites]
Interesting.
Fractal compression was particularly interesting (but superseded by DCT-based compression - JPEG, MP3, etc) these days.
Arthur C. Clarke is sporting a weird hybrid of Dr. Evil and North Korean Dictator chic.
posted by flippant at 4:39 AM on April 3, 2014
Fractal compression was particularly interesting (but superseded by DCT-based compression - JPEG, MP3, etc) these days.
Arthur C. Clarke is sporting a weird hybrid of Dr. Evil and North Korean Dictator chic.
posted by flippant at 4:39 AM on April 3, 2014
Pretty sure they're replicating Mr Clarke in a bifurcated fashion.
posted by panaceanot at 5:31 AM on April 3, 2014
posted by panaceanot at 5:31 AM on April 3, 2014
A fine demonstration to the limits of early 90s film catalog music. When Clark first dives into the set, the wanging guitar skibble feels all wrong. Everyone knows Mandelbrot set sounds like acid house!
posted by bendybendy at 5:43 AM on April 3, 2014 [1 favorite]
posted by bendybendy at 5:43 AM on April 3, 2014 [1 favorite]
> Everyone knows Mandelbrot set sounds like acid house!
I thought it sounded like Jonathan Coulton.
posted by Foosnark at 6:25 AM on April 3, 2014 [1 favorite]
I thought it sounded like Jonathan Coulton.
posted by Foosnark at 6:25 AM on April 3, 2014 [1 favorite]
Wanging guitar skibble ?!? Bite your tongue. That is David Gilmour CBE Kind of nice actually - reminds me of pre DSOTM Floyd.
posted by sea at 7:18 AM on April 3, 2014
posted by sea at 7:18 AM on April 3, 2014
Thank goodness someone reframed the video to fit my wide-screen TV. I love when they cut off the top and bottom almost as much as when they stretch the picture horizontally (although neither method is as awesome as pan-and-scan, from the olden days).
In case any weirdos want to see the full picture in its "correct" aspect ratio, here's the link to that.
posted by LEGO Damashii at 7:54 AM on April 3, 2014 [2 favorites]
In case any weirdos want to see the full picture in its "correct" aspect ratio, here's the link to that.
posted by LEGO Damashii at 7:54 AM on April 3, 2014 [2 favorites]
You can feel the strong tug on the mathematicians' minds where they want their math to be descriptive of physical reality. They want what they see in their math to be a fundamental rule of reality.
The equation of a fractal assumes it's infinite. zn+1 = zn2 + c says how to get the n+1th element from the nth, with nothing there about any stopping point.
The mathematicians jump from their assumption of infinite extent to an assertion that the universe goes on infinitely. But they back off. They bring in Stephen Hawking to say no, the universe doesn't go to infinitely small size, it's limited by the Planck length.
They didn't bring in a developmental biologist to also say that, though ferns and trees might resemble certain fractals, they are not built by simple rules repeated fractal-wise.
Each freckle on a human body has its location specified by a particular bit of DNA corresponding to that freckle, remarkably. There are some cases where formulaic repetition happens, like polka-dotted patterns on a butterfly wing where, over a limited stretch of wing, the DNA might give an instruction that works out to "repeat this sequence of chemical concentrations until it runs into this other chemical gradient." That might result in 9 spots for a particular butterfly, without the number being specified. But much more usually, if there are 9 spots, then there are 9 pieces of DNA, each piece corresponding to one of the spots.
It's nothing like the automatic repetition of a fractal. The difference is so striking that it's remarkable to see these mathematicians reaching for a connection with their math when the natural phenomena are so radically different.
This documentary is from 1994. Fractals were pretty new, and the detailed mechanisms from DNA to developed bodies weren't known. Interesting to see this example of how people tend to think during the first flush of enthusiasm over a new idea, when the possibilities seem limitless (i.e., they "trip the fuck out" like loquacious said).
posted by kadonoishi at 8:07 AM on April 3, 2014 [2 favorites]
The equation of a fractal assumes it's infinite. zn+1 = zn2 + c says how to get the n+1th element from the nth, with nothing there about any stopping point.
The mathematicians jump from their assumption of infinite extent to an assertion that the universe goes on infinitely. But they back off. They bring in Stephen Hawking to say no, the universe doesn't go to infinitely small size, it's limited by the Planck length.
They didn't bring in a developmental biologist to also say that, though ferns and trees might resemble certain fractals, they are not built by simple rules repeated fractal-wise.
Each freckle on a human body has its location specified by a particular bit of DNA corresponding to that freckle, remarkably. There are some cases where formulaic repetition happens, like polka-dotted patterns on a butterfly wing where, over a limited stretch of wing, the DNA might give an instruction that works out to "repeat this sequence of chemical concentrations until it runs into this other chemical gradient." That might result in 9 spots for a particular butterfly, without the number being specified. But much more usually, if there are 9 spots, then there are 9 pieces of DNA, each piece corresponding to one of the spots.
It's nothing like the automatic repetition of a fractal. The difference is so striking that it's remarkable to see these mathematicians reaching for a connection with their math when the natural phenomena are so radically different.
This documentary is from 1994. Fractals were pretty new, and the detailed mechanisms from DNA to developed bodies weren't known. Interesting to see this example of how people tend to think during the first flush of enthusiasm over a new idea, when the possibilities seem limitless (i.e., they "trip the fuck out" like loquacious said).
posted by kadonoishi at 8:07 AM on April 3, 2014 [2 favorites]
Each freckle on a human body has its location specified by a particular bit of DNA corresponding to that freckle, remarkably.
This certainly would be remarkable if it held the slightest bit of truth. The opposite is solidly known to be the case in many specific cases, such as zebra stripes and brain development (which is ultimately so complex the genome would have to be tens of thousands of times larger than it is in order to micro-manage its growth).
posted by localroger at 8:28 AM on April 3, 2014 [4 favorites]
This certainly would be remarkable if it held the slightest bit of truth. The opposite is solidly known to be the case in many specific cases, such as zebra stripes and brain development (which is ultimately so complex the genome would have to be tens of thousands of times larger than it is in order to micro-manage its growth).
posted by localroger at 8:28 AM on April 3, 2014 [4 favorites]
Um, yes, there are some cases where formulaic repetition happens. Are you sure about the zebra stripes? I don't have my copy of "Endless Forms Most Beautiful" handy, but I seem to remember Carroll discussing individual zebra stripes as each being controlled by a specific DNA switch.
posted by kadonoishi at 8:34 AM on April 3, 2014 [1 favorite]
posted by kadonoishi at 8:34 AM on April 3, 2014 [1 favorite]
re: math, physics and biology
cheers!
posted by kliuless at 8:45 AM on April 3, 2014 [3 favorites]
First, consider a leaf. In The Formation of a Tree Leaf by Qinglan Xia, we see a possible key to Nature's algorithm for the growth of leaf veins. The vein system, which is a transport network for nutrients and other substances, is modeled by Xia as a directed graph with nodes for cells and edges for the "pipes" that connect the cells. Each cell gives a revenue of energy, and incurs a cost for transporting substances to and from it.more on fractal math (and maybe physics ;)
The total transport cost depends on the network structure. There are costs for each of the pipes, and costs for turning the fluid around the bends. For each pipe, the cost is proportional to the product of its length, its cross-sectional area raised to a power α, and the number of leaf cells that it feeds. The exponent α captures the savings from using a thicker pipe to transport materials together. Another parameter β expresses the turning cost.
Development proceeds through cycles of growth and network optimization. During growth, a layer of cells gets added, containing each potential cell with a revenue that would exceed its cost. During optimization, the graph is adjusted to find a local cost minimum. Remarkably, by varying α and β, simulations yield leaves resembling those of specific plants, such as maple or mulberry.
A growing network.
Unlike approaches that merely create pretty images resembling leaves, Xia presents an algorithmic model, simplified yet illuminating, of how leaves actually develop. It is a network-theoretic approach to a biological subject, and it is mathematics—replete with lemmas, theorems and algorithms—from start to finish...
cheers!
posted by kliuless at 8:45 AM on April 3, 2014 [3 favorites]
Further reading:
posted by No Robots at 8:52 AM on April 3, 2014
- Fractal Physiology
- Fractal Geometry in Biological Systems: An Analytical Approach
- Fractal Modelling: Growth and Form in Biology
posted by No Robots at 8:52 AM on April 3, 2014
Proof of Arthur C. Clarke's genius lies in the selection of David Gilmour as musical accompaniment.
posted by GrapeApiary at 10:12 AM on April 3, 2014
posted by GrapeApiary at 10:12 AM on April 3, 2014
Each freckle on a human body has its location specified by a particular bit of DNA corresponding to that freckle, remarkably.
There is no DNA that specifies where freckles will be positioned on the skin. Freckles come about through a hormone signal that binds to a cell membrane-bound receptor protein, which in turn triggers melanin production. UV light brings more receptors to the cell surface and stimulates melanin-producing cell production, which both amplify pigmentation.
posted by Blazecock Pileon at 11:00 AM on April 3, 2014 [3 favorites]
There is no DNA that specifies where freckles will be positioned on the skin. Freckles come about through a hormone signal that binds to a cell membrane-bound receptor protein, which in turn triggers melanin production. UV light brings more receptors to the cell surface and stimulates melanin-producing cell production, which both amplify pigmentation.
posted by Blazecock Pileon at 11:00 AM on April 3, 2014 [3 favorites]
Fractal compression was hilariously close to a fraud, since there's no way to invert these highly nonlinear iterated functions to go from an image to a small set of parameters that would generate a similar image. The only method is exhaustive search, which given unlimited time could also get you perfect “Kolmogorov compression” of any data by searching for the shortest program that would output a given string of bits.
IIRC it turned out that the initially promising results all involved significant human effort.
(The reason other approaches like DCT, wavelets, etc. were successful is not their degree of compression, but rather their predictable runtime.)
posted by mubba at 7:10 PM on April 3, 2014 [2 favorites]
IIRC it turned out that the initially promising results all involved significant human effort.
(The reason other approaches like DCT, wavelets, etc. were successful is not their degree of compression, but rather their predictable runtime.)
posted by mubba at 7:10 PM on April 3, 2014 [2 favorites]
Oh nice. Thanks, loquacious.
posted by homunculus at 8:21 PM on April 3, 2014
posted by homunculus at 8:21 PM on April 3, 2014
-The Formation of a Tree Leaf
-The Formation of A Tree Leaf
posted by kliuless at 8:00 AM on April 4, 2014
-The Formation of A Tree Leaf
posted by kliuless at 8:00 AM on April 4, 2014
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