Ralph Melton ([info]ralphmelton) wrote,
@ 2009-06-25 16:32:00
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Fractal Pecan Pie
This quote from http://www.instructables.com/id/giant-fractal-pecan-pie/ reminded me of [info]eub:
the thing they don't tell you about fractals is just how sharp and dangerous they are. i mean, you think you have a pretty good grasp of the mathematical analysis but until a piece of metal with a very high perimiter to surface area ratio tears into your flesh, you're really missing intuitive appreciation for objects that lack continuous derivatives almost everywhere.

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[info]eub
2009-06-26 06:08 am UTC (link)
That's very pretty, but doesn't it still have the problem they're trying to address, that filling asymptotically dominates crust? Linear pie is ho-hum but gets the job done.

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[info]katybeth
2009-06-26 06:33 am UTC (link)
That was pretty much exactly my thought. For a large pie, you really need something with a lot of interior edges. Or just make lots of small pies, of whatever shape.

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[info]eub
2009-06-26 06:36 am UTC (link)
SierPIEnski gasket?

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[info]ralphmelton
2009-06-26 09:46 pm UTC (link)
Man, it took me five or six reads before I spotted the pun. Before that, I was just going to make a foolish remark about how I preferred my pie to have positive measure.

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[info]ralphmelton
2009-06-26 09:43 pm UTC (link)
In a mathematical abstraction, it solves the stated problem, since the fractal has infinite perimeter. If the crust is really 'the portion of pie within a crust-width of the edge', not so much.

I think they are defining the problem improperly, though--if you're trying to make sure that every piece of pie has a good amount of crust, the proper measure is the radius of the inscribed circle. (And if that's your measure, that's best achieved by linear pie or pie with lots of interior angles, like the all-edge brownie pan.)

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