Print PDF
Favorite
Email
For π day this year, I thought it would be fun to make a fractal design based on circles - an Apollonian Gasket. The flavor choice then seemed obvious - apple and onion, right?! My hope was to make a fractal that was both space filling AND stomach filling as well! I had never made a savory pie before, but after browsing the interwebs for some ideas I was convinced that this filling had merit (especially with bacon...) and decided to give it a try.
I also like to support my Farmer's Market, so the apple, onion, cheese, and duck prosciutto were all purchased there from local farmers.
To get started you will need the following ingredients:
Cheese Dough : (enough for 2 pie dishes)
2 1/2 cups unbleached all-purpose flour
1 teaspoon salt
1 teaspoon sugar
1/2 cup fresh grated parmesan
8 oz (2 sticks) unsalted butter
8-10 tablespoons ice water
Filling :
3 slices thick cut bacon or thin-sliced prosciutto, chopped
1 yellow onion, medium, sliced
1 Granny Smith apple, medium, peeled and sliced
2 eggs
3/4 cup milk
1/8 teaspoon fresh grated nutmeg
1/2 teaspoon ground red pepper
1/2 teaspoon smoked paprika
Fresh cracked black pepper to taste
3/4 cup fresh grated cheese (either parmesan or Gruyere)
2 tablespoons olive oil (if using prosciutto)
Equipment / Tools
I also used a 9.5 inch pie dish, cutting board, cooling rack, rolling pin, cookie sheet, cheese grater, pie weights (or beans), and a large food processor for the pie.
To design the crust I used parchment paper, a compass, an accurate ruler (up to 1/16th inch), a sharp knife, and a spreadsheet for some quick number crunching.
I also like to support my Farmer's Market, so the apple, onion, cheese, and duck prosciutto were all purchased there from local farmers.
To get started you will need the following ingredients:
Cheese Dough : (enough for 2 pie dishes)
2 1/2 cups unbleached all-purpose flour
1 teaspoon salt
1 teaspoon sugar
1/2 cup fresh grated parmesan
8 oz (2 sticks) unsalted butter
8-10 tablespoons ice water
Filling :
3 slices thick cut bacon or thin-sliced prosciutto, chopped
1 yellow onion, medium, sliced
1 Granny Smith apple, medium, peeled and sliced
2 eggs
3/4 cup milk
1/8 teaspoon fresh grated nutmeg
1/2 teaspoon ground red pepper
1/2 teaspoon smoked paprika
Fresh cracked black pepper to taste
3/4 cup fresh grated cheese (either parmesan or Gruyere)
2 tablespoons olive oil (if using prosciutto)
Equipment / Tools
I also used a 9.5 inch pie dish, cutting board, cooling rack, rolling pin, cookie sheet, cheese grater, pie weights (or beans), and a large food processor for the pie.
To design the crust I used parchment paper, a compass, an accurate ruler (up to 1/16th inch), a sharp knife, and a spreadsheet for some quick number crunching.
Remove these ads by
Signing UpStep 1Making a Fractal
The crust design is an Apollonian Gasket. Wikipedia has a great article all about Apollonian Gaskets
http://en.wikipedia.org/wiki/Apollonian_gasket
The essential things to know are:
- An Apollonian Gasket is a space-filling fractal. In theory you could make many more circles to continue to fill the top of the pie, but in practice I found that 16 provided a nice design and kept circles at a reasonable size to work with.
- Curvature is how "sharp" a curve is, and is inversely proportional to the radius of curvature . A straight line would have an infinite radius of curvature, the edge of a large circle would curve slowly (low curvature, large radius), while a small circle would curve very quickly (high curvature, small radius). The designs shown on Wikipedia list the relative curvatures of the circles within the fractal (with the first, negative, number listed being the radius of the largest "frame circle"), so we need to do a little number-crunching to figure out the actual radii we want to use.
I decided to use the {-12, 25, 25, 28, 48} pattern that is shown on Wikipedia (I prefer the almost-D3 symmetry). To calculate the radii of the circles you will use, you need to take the radius of your pie dish (my 9.5 in dish has a 4.25 in radius), and multiply that radius by the first number in the pattern (in my case 12, the negative number) then divide by the curvature in question.
The pattern I chose to follow
http://en.wikipedia.org/wiki/File:ApollonianGasket-12_25_25_28-Labels.png
For example, to find the radius of the "25" circle in the pattern, I used my spreadsheet to multiply 4.25 in * 12 / 25 = 2.28 in, or approximately 2 + 4/16 inches. If you are using a different sized pie dish, you can take each number below, multiply it by the diameter of your pie dish, and divide by 9.5
The radii, in inches, for the sixteen circles I used are as follows
Curvature Radius (decimal) Radius (fraction)
25 2.280 2 4/16
25 2.280 2 4/16
28 2.036 2 1/16
48 1.188 1 3/16
57 1.000 1 0/16
57 1.000 1 0/16
97 0.588 0 9/16
97 0.588 0 9/16
112 0.509 0 8/16
112 0.509 0 8/16
121 0.471 0 8/16
121 0.471 0 8/16
168 0.339 0 5/16
208 0.274 0 4/16
232 0.246 0 4/16
232 0.246 0 4/16
Once you calculate the radii of the circles you intend to cut out, use your trusty compass to carefully measure off each radius on the ruler, then draw the circles on a large sheet of parchment paper. Do NOT cut them out yet. I also found it helpful to label each circle by its curvature, for reference later...
http://en.wikipedia.org/wiki/Apollonian_gasket
The essential things to know are:
- An Apollonian Gasket is a space-filling fractal. In theory you could make many more circles to continue to fill the top of the pie, but in practice I found that 16 provided a nice design and kept circles at a reasonable size to work with.
- Curvature is how "sharp" a curve is, and is inversely proportional to the radius of curvature . A straight line would have an infinite radius of curvature, the edge of a large circle would curve slowly (low curvature, large radius), while a small circle would curve very quickly (high curvature, small radius). The designs shown on Wikipedia list the relative curvatures of the circles within the fractal (with the first, negative, number listed being the radius of the largest "frame circle"), so we need to do a little number-crunching to figure out the actual radii we want to use.
I decided to use the {-12, 25, 25, 28, 48} pattern that is shown on Wikipedia (I prefer the almost-D3 symmetry). To calculate the radii of the circles you will use, you need to take the radius of your pie dish (my 9.5 in dish has a 4.25 in radius), and multiply that radius by the first number in the pattern (in my case 12, the negative number) then divide by the curvature in question.
The pattern I chose to follow
http://en.wikipedia.org/wiki/File:ApollonianGasket-12_25_25_28-Labels.png
For example, to find the radius of the "25" circle in the pattern, I used my spreadsheet to multiply 4.25 in * 12 / 25 = 2.28 in, or approximately 2 + 4/16 inches. If you are using a different sized pie dish, you can take each number below, multiply it by the diameter of your pie dish, and divide by 9.5
The radii, in inches, for the sixteen circles I used are as follows
Curvature Radius (decimal) Radius (fraction)
25 2.280 2 4/16
25 2.280 2 4/16
28 2.036 2 1/16
48 1.188 1 3/16
57 1.000 1 0/16
57 1.000 1 0/16
97 0.588 0 9/16
97 0.588 0 9/16
112 0.509 0 8/16
112 0.509 0 8/16
121 0.471 0 8/16
121 0.471 0 8/16
168 0.339 0 5/16
208 0.274 0 4/16
232 0.246 0 4/16
232 0.246 0 4/16
Once you calculate the radii of the circles you intend to cut out, use your trusty compass to carefully measure off each radius on the ruler, then draw the circles on a large sheet of parchment paper. Do NOT cut them out yet. I also found it helpful to label each circle by its curvature, for reference later...
| « Previous Step | Download PDFView All Steps | Next Step » |
4
comments
|
Add Comment
|
1
Nov 27, 2011. 10:16 PM
una_amor
says:
una_amor
says:
OMG I love the ingredients in this gem. Going to make it for sure!
Reply
32
Nov 27, 2011. 10:02 AMiminthebathroom
says:
iminthebathroom
says:
Love flavours like this together, awesome
Reply
111
Nov 27, 2011. 9:19 AMjessyratfink
says:
jessyratfink
says:
Sounds amazing and it's beautiful too! :)
Reply
Mar 20, 2011. 6:14 AMphragments
says:
Perfectly delicious for brunch, rounded off with champagne.
Reply
 |
Add Comment
|
