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 R2 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.