Registered: Aug 2003
Posts: 712

Which made this organic-looking (if somewhat alien) shape? Since it is nothing but ice on a hubcap, it would appear it has to be the former. Nothing artistic or arranged - it was noticed (by Eric Weisstein, creator of Mathworld, as it happens) - not made.

For seasonal amusement value...

Jason Cawley has attached this image:

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Registered: Oct 2003
Posts: 167

Jason, the longer I stare at that wonderful little artefact of nature, the more I am reminded that there might always be more going on than pure simple rules can account for.

I'm not long back from an annual vacation a lot closer to the wonderful fine detail of the natural world, thankfully at somewhat warmer temperatures.

While I'm all too familar with the fact that simple rules can produce forms which are reminiscent of natural forms, there are always other things going on so the matches rarely approach perfection.

So this only makes me more interested in the notion that nature's rules may be incompletely defined. Finding an explanation for that incompleteness that is a bit more useful than just assuming intrinsic randomness may be a hard problem, but that does not mean we should avoid it.

As always, there seems to be something about fluids, in particular their angular isotropy, which really test the notion of fully discrete fully deterministic rules.

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Tony Smith
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Registered: Mar 2004
Posts: 132

Tony, you're right about finding an explanation for that incompleteness. The problem here is that while natures rules may be incompletely defined by simple ones, adding in any more features would make the rule too complex as a model.

I think that using models with live input, of which I've discussed using cellular automata here, is exactly the kind of approach we need if we are ever going to make meaningful models of, say, some complex biological process where the pertubation is more than random, or this ice anemone even.

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