I was 8 years old when I walked into a department store dressing room and watched in amazement as my reflection bounced back and forth recursively between two parallel mirrors. It was my first glimpse of infinity and though I didn't know it then, I was looking at a fractal.
In 1958, Benoit Mandelbrot, a brilliant young mathematician joined the research staff at IBM. As one of the first mathematicians to have access to high-speed computers, Mandelbrot conceived and developed a radical new geometry that was capable of mathematically describing the real world of Nature. In 1982, he published his ideas in "The Fractal Geometry of Nature" and rocked the world.
Before fractals (which also became known as Chaos Theory), Euclidian geometry was concerned with the abstract perfection that was nearly non-
existent in Nature. It could only describe the imaginary world made up of zero (a single point), the first dimension (a single line that contains an infinite number of points), the second dimension (a plane that contains an infinite number of lines), and the third dimension (a solid that contains an infinite number of planes). None of these could describe the amorphous and irregular shape of a cloud, mountain, coastline or tree. Mandelbrot's fractals were capable of describing the real world of the fourth dimension (a hypercube that contains an infinite number of solids and their relationship to each other in a time-space continuum). The fourth dimension is the world in which we live.
The mathematics of fractals are relatively simple, considering that they describe the indiscernibly complex. Fractals are geometric figures that repeat themselves under different levels of magnification. They are self-similar and recursive. An example would be the irregular and jagged shape of a mountain when viewed from a distance. When a section is magnified, the same shape or pattern is repeated with greater complexity. The pattern repeats itself with increasing detail as it goes on to be magnified to a microscopic scale. Fractals reveal the hidden worlds within a world.
But what about food and cooking?
Certainly, food, be it plant or animal, contain fractal patterns. A perfect example is the beautiful and alien-looking Romanesco cauliflower, whose spires swirl repeatedly in various scales over the pale green heads. An example of a fractal–in a prepared food–would be a turducken (a chicken stuffed in a duck, stuffed in a turkey). And isn't a salad just a vegetable recursion?
As for cooking, could the act of whipping, which is a repetitive motion that changes the volume and texture of a substance with a self-similar expansive network of air bubbles, be fractal? If so, then couldn't the same be true of a reduction? And what about the turns required to make puff pastry? Or the gluten matrix produced in bread by carbon dioxide and ethyl alcohol?
Would fractal flavor involve repeating a flavor in varying proportions/scales, such as a sandwich where each bite contains the same flavors and textures in slightly different proportions? Or a glass of wine that is a liquid composition of complex flavors and with each sip, we can discern, or magnify, a different element of its flavor? Would a dish composed of self-similar aroma compounds be a flavor fractal? Or one composed of the same flavor in varying textures?
My preoccupation with these questions can, in and of itself, be considered fractal as I zoom in for clarity and answers, I only find more detail and questions. Ultimately, I believe it is a search for connectivity… to myself, to others, to the physical world as well as the spiritual, and, of course, to food.
Soy fractal
fresh soybeans: edamame cone
dried soybeans: soy milk foam (using inherent lecithin in soy)
tofu sphere (with malt)
yuba cylinder (with peanut, miso, and okara)
fried yuba
fermented soy: sweet shoyu sauce
douchi soil
natto
self-similar aromas: soy, peanut, malt (alcohols: sulfurol
guaiacol
aldehydes: valeraldehyde
butyraldehyde
fatty acids: butyric acid
isovaleric acid)
Playing with Fire and Water 
Oh my goodness, this entry is absolutely amazing. The literature behind it (because the inner mathemetician in me is excited to read about fractals) and the cooking is certainly a potent combination.
That said — this dish just seems to be a plate containing the myriad forms of the same bean. How does this dish differ from a plate full of a variety of chocolates or a plate that shows the different parts of corn or… I think you get the idea.
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I am so impressed that you have woven in fractals into a cooking blog. Plants are so close to fractals that in computer graphics they are modeled by a subclass of fractals called L-systems. I just love to stare at the Romanesco broccoli, it’s mesmerizing.
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