This week I’ve been investigating fractals.
I’ll give you some examples of everyday fractals to get us started. See if you can find the common thread.
Snowflakes, snails, ferns.
Yup, each of these is made up of identical reoccurring shapes. That shape is based on an equation formulated by a French mathematician named Mandelbrot.
Wikpedia elaborates: “Images of the Mandelbrot set exhibit an … infinitely complicated boundary that reveals progressively ever-finer recursive detail. … The set’s boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.”
Got that?
“The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules.”
Mandelbrot’s equation says it all: zn+1 = zn2 + c. I’m told that it’s a thing of beauty.
Not all leaves, lightning bolts and shells are fractals, but a significant number are. All snowflakes are, and so are all escargots (the snail and the begonia).
And so, most spectacularly in my view, and what got me started on my fractal journey, is the Romanesco cauliflower.
Some taxonomists call it by the common name of its cousin, broccoli, which it resembles more closely from a mathematical point of view. But the horticultural similarity is closer to cauliflower, by virtue of its taste.
Romanesco cauliflower isn’t just fascinating to look at — it’s also deliciously nutty and crunchy on the tooth.
I bought my first head last week. I was shopping at Mississippi Market with one of my daughters. She is in the nutrition business. Her company blends healthful raw vegetables and fruits into supplements that are labeled “plant-based.” Her powders’ main ingredient is caffeine. Half-marathons are a snap when you’ve just ingested the equivalent of a pot of espresso.
That espresso itself is plant-based means that being buzzed is not on its face a bad thing. Nor is it the whole thing. The other plants lend flavor and antioxidants.
I wouldn’t recommend plant-based energy drinks to someone with a heart condition, though, especially if that someone were stimulated to run a marathon. In fact, I would suggest anyone interested in these products get in shape before they place their order.
Romanesco cauliflower is one of the trendier foodstuffs among fitness-obsessed foodies who live in Brooklyn. It is happiest growing outdoors in California. There it can be cultivated all year-round. I plan to grow it next summer. It combines many of my favorite aesthetic attributes. Picture Angelina sedum. It’s almost a dead ringer, though Romanesco cauliflower isn’t made up of miniature bristles. Its color is chartreuse but its structure is fractal.
Imagine a Russian nesting doll. You open the doll and find its twin inside, a hair smaller but big enough to house its twin again, which is again a hair smaller but big enough to house still another slightly smaller twin …
So if this doll were a Romanesco cauliflower, it would not hide its fractal self but show it off. Each new fractal grows out of, or off, the preceding one.
Each is actually a flower bud. The flower buds begin microscopically tiny and expand, then grow the next one, and so on.
When the whole head of cauliflower is analyzed under a microscope (or even without one) the growth pattern is quite visible. And also flawlessly perfect. Miraculous, in its way.
Why are some things fractal and others not? Fractals are just one of many thousands of ways living things evolve to survive and thrive in a particular habitat. The vessels and arteries in the human body are fractal, in that the major vessels branch out in ever smaller but identical tributaries to enable the most blood to get into the tightest spaces in the shortest time.
Fractal forms are advantageous in the wild because they expose the plant to light from as many angles as possible. This is why Romanesco cauliflower can grow in a place that gets limited light (it still technically needs full sun). Its fractals are shaped like triangles.
Not all fractals are.
The Koch snowflake, for instance, is shaped like a circle whose six bump-outs are each composed of six identical though miniature bump-outs, whose six bump-outs are … well, you know.
Likewise, the curving shape of the escargot shell (or leaf, if the escargot is a begonia plant) is not a triangle but a curve that spirals seemingly into infinity, the slightly widening arc of the spiral enabling that perpetual growth to occur.
Outer space is full of fractals and may even BE a fractal, for all I know.
My preferred area of focus is the knowable. I am a gardener. If I can find seeds for Romanesco cauliflower (its botanical name is Brassica oleracea), I will start them indoors early. It takes 80 to 90 days for a plant to mature.
I haven’t tried eating the one my daughter made me buy. We take our holiday meals at various relatives’ homes, where the annual contribution from me is not in the veggies category but dessert. I make a kickass Yule Log.
This year’s log was 3 feet long. I had to give it a couple of curves to make it fit on the black poster board I used as a serving platter. The log was decorated with chocolate kisses to evoke mushrooms and powdered sugar for new-fallen snow.
The final touch was, if I may say so, brilliant. For the conifer seedlings one often finds sprouting on the forest floor near dead logs gathering moss and fungi, I used Romanesco cauliflower fractals.
Each was dipped in Elmer’s glue so it wouldn’t slide off the board. The relatives gaped in horror at the log, which did resemble a live alligator more than it did a dead tree.
I didn’t ask them how the cauliflower tasted. It wouldn’t have been a fair question. Even a vegetable as nutritious as Cauliflower “Veronica” (this is the cultivar my daughter selected), can’t compete with rolled chocolate cake filled with whipped cream and drenched in hot fudge sauce.
Come to think of it, though, there was something similar about that rolled cake. I wonder if it’s fractal.
