Monday, 21 April 2008

Sierpinski (fractal) biscuits

A little while ago BoingBoing, a "directory of wonderful things" which I read quite often, featured an article on how to make fractal cookies. The original article with instructions is at Evil Mad Scientist Laboratories. Well, I couldn't resist, and of course for a challenge opted to make Sierpinski triangle biscuits, where they made a (square cross-section) Sierpinski carpet.

Well, I say square, but of course since these are fractals, they actually have Hausdorff dimensions of log 8/log 3 ≈
1.8928 and log(3)/log(2) ≈ 1.585 for the carpet and "triangle" respectively, and no area. I take no responsibility if, as a result, the cookies are tasteless or those eating them are sucked into fractional dimensional space...

The recipe:

For this recipe you will need two different coloured biscuit doughs. The Mad Scientists used chocolate and plain vanilla, but I chose to add red colouring and orange essence to the vanilla. The original recipe is derived from an Instructable on making pixel cookies, with modifications for the chocolate. I have provided recipes for both doughs, with measurements in metric, and instructions that don't require a Kenwood. (I really don't think many people outside the United States have the vaguest clue how much butter a "stick" is.)

Vanilla mix

(or whatever flavour you choose)

2.5 cups flour,
3/4 cups caster sugar
1/4 tsp salt
225g butter
2tsp vanilla extract
2tbs cream cheese, softened
(about 2tsp of another essence and/or food colouring if you choose)

Chocolate mix

2 1/4 cups flour,
1/4 cup of cocoa powder
3/4 cups caster sugar
1/4 tsp salt
1 tbs melted chocolate
210g butter
2tsp vanilla extract
2tbs cream cheese, softened
(about 2tsp of another essence and/or food colouring if you choose)

Making the dough

  1. Mix the dry ingredients, sifting the flour if necessary.
  2. Rub in the butter.
  3. Mix in the cream cheese and vanilla (and chocolate, if applicable) - this will require some kneading to get the dough right.

Making the fractals

The mad scientist article has quite good instructions. If you have difficulty imagining how to do the triangle, here's an example of them doing it with Fimo clay.


  • Don't let the chocolate get too hot. It's a very small amount, so using a double boiler is ideal (though if you're lazy like me you'll use a microwave). Like me, you may also burn the chocolate...
  • The chocolate dough is more crumbly than the vanilla (possibly in part because I burned it, but possibly because cocoa just doesn't have the same properties as flour). Anyway, be more careful with it. You're likely to have more success with fractals that use the chocolate as the "main" (big inner triangle) colour.
  • Use a very sharp knife to cut the biscuits. I used my hand-forged usuba bocho.
  • If you don't know how to rub butter, BBC Food has instructions.
  • I made half quantities of each of the doughs, but make the whole lot if you have some time (and want to end up with a lot of biscuits) on your hands.

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