## Introduction: Giant Fractal Pecan Pie

for thanksgiving 2k4 we opted to construct a very large pie.

based on a prototype the previous year we were aware of a fundamental limitation of large pies, namely the crust to filling ratio. for traditional circular pies of radius R, the amount of filling scales as R^{2} while the crust only scales linearly so as the pie grows larger, the flaky crust is completely dominated by the creamy filling.

our solution was to construct a pie pan in the shape of a koch snowflake (whose perimter obeys completely different scaling laws), fill it with delicious pecan pie and bake in a custom backyard oven.

## Step 1: Layout Design

the layout was determined by two constraints:

1. the finished product had to fit in the transport vehicle. this gave an maximum outside diameter of around 50 inches, conveniently close to the 24x48 inch sheet metal available at the local hardware store. this set the initial side length L of the largest triangle.

2. we only had access to crust of a finite constant thickness so the smallest triangle had to contain some reasonable amount of filling. (L/3)^{niter > minimum acceptable edge length suggested that we go no deeper}

than 4 iterations.

A template covering (1/12) of the entire perimiter made reasonably quick work of laying out the pie pan edge.

## Step 2: Cut Sheet Metal to Shape

shaping was conducted entirely with handtools, a shear and a nibbler. at least 10 hours and many blisters later the 768 sided outline began to look like a reasonable approximation to an approximation of a fractal.

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.

## Step 3: Attach Rim

the rim was fabricated out of much lighter weight material than the base. flexible enough to fold cleanly and match our template. unfortunately, it was too thin to weld in any clean way and was galvanized to boot. an afternoon at the crucible (http://www.thecrucible.org/) with a tig torch left me with a bad case of "zinc metal madness" and a rim which was loosley attached in the ugliest of ways.

tip: using a pair of needle nose pliers to press down hard on the tabs as they were being welded helped to conduct heat into the thicker base giving more even heating of both parts and keeping the thiner part from burning away.

## Step 4: Build Oven

the oven was simply a pile of cinder blocks and a propane burner (seasonal item adapted from a turkey fryer). a sheet of durock made for a lid and base. there was no reason it had to be physically possible for this construction to reach pie appropriate tempuratures but the heat loss ended up being low enough and the propane valve controllable enough that we could easily maintain the 350-400 F required for baking. rather good luck as we didn't have a backup plan.

## Step 5: Make Crust

aluminum foil lined the pan and hopefully protected us from the not-so-foodsafe construction. crust was a traditional recipe. cut cold butter into flour and add a little ice water as necessary to make dough. minimal kneading needed. the tiny pockets of butter melt and boil during the baking process giving the coveted flakyness of a good pie crust

## Step 6: Mix Filling

a careful calculation gave us the appropriate amount of filling, approximately 21 standard pies worth. the filling recipie was based on a previous attempt which averaged the ingredients of 5 different pecan pie recipies from the web. this assumption of local linearity in the space of pies seemed to work out well.

## Step 7: Cook

cooking took about an hour and a half. the pie was of standard thickness so the appropriate cooking time was only slightly longer than the standard hour (in part due to the longer time required to get the oven up to temperature). the only real difficulty here was leveling as the filling flows towards the low end of the pie.

the uphill portion which (was also directly over the burner) ended up somewhat overcooked and dry but heat distribution was suprisingly uniform and the results completely edible.

## Step 8: Enjoy

crust enough for the most serious connoisseur. the pie pan was only used once but lingers on as a wall hanging.

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## 44 Comments

This Instructable was featured on NPR's Here & Now on November 24, 2008!

While the pie is amazing in and of itself (my jealousy knows no limits - having nut allergies SUCK around the holidays as my family makes absolutely amazing pecan pies. There are days I seriously ponder the pros/cons of saying to heck with it and having a slice, after all, I've GOT an epipen... haven't buckled yet, but the idea is always there) the part that has me furiously scribbling and trying to work out some details is the giant oven you created. I'm suddenly seeing potential for backyard pizza parties where one pizza really IS all that is needed for 20 people! Or perhaps an epic brownie to end all brownies?

kochs curve

This is super cool, and now I want to make decorative fractal art!

Best paragraph I've read in a while. Found my way through: http://felixsalmon.tumblr.com/post/13577123646/the-thing-they-dont-tell-you-about-fractals-is

That's just totally AWSOME !!!!

Thanks so much for sharing it all, the PIE PAN, the OVEN ,

& most of all THE PIE !!! Sincerely, Jus Beachy

Beautiful pie! Granted, you've achieved a pie with a more crustacous scaling law, but how do you serve it in human-sized pieces, assuring each diner a similar quantity of crust? The problem would be easy to fix in a purely mathematical sense, in the same way that a sphere can be dissected and reassembled into two spheres. The trick doesn't work for real representations of spheres, and sadly, probably wouldn't work for real pies, either. :( Maybe a Sierpinski gasket-shaped pie pan?

Sierpinski gasket pie...

Maybe a Menger sponge cake (or Menger spongecake, w/e)

Of course it would soak up a lot of rum (infinite surface area) but would not be very filling (with zero volume)

dear god... infinite pie...

i understand what you are trying to do with the whole "filling dominates crust" thing, but wouldnt the midlle be dominated? i guess you could solve this by making the center a bit thicker than the edges. Please reply, as i would like to know what you think about it. Thanks, -Darthpotato