Chaotic Utopia

Friday Fractal XXV


Occasionally, I run across a fractal in nature that is so perfectly formed, that the repeating, scaling patterns are actually 3-D. In these cases, it is difficult to do the image justice by creating a similar fractal on a 2-D surface. I encountered this in today’s fractal. The Julia set, colored with a formula named Azar por Amplitud (literally, chance by amplitude) by Marcelo Anelli, mimics nature to some degree:


But doesn’t reach nearly the fractal depth of field found in this vegetable:


Broccoli Romanesco (Brassica oleracea var. Botrytis) florets (photo by Alfredo Matacotta)

(Ok, I know you’re probably tired of food, after a huge Thanksgiving dinner, but at least this makes that leftover broccoli salad in the fridge look more interesting.)


Broccoli has become almost as famous for displaying fractal patterns as it has for grossing out children at the dinner table. (I’ll confess, while I adore these patterns, I was one of the kids who turned their nose up at the stuff.)

If you’re still hungry for more, John Walker of Fourmilab, Switzerland, has an excellent description of this variety of the cabbage family, along with more striking images. He discusses not only the fractal forms of the vegetable, but also which branch of the cabbage family it might belong to, (cauliflower, broccoli, or unique cabbage?) caloric information, and the best ways to serve it up for a snack.

Broccoli Romanesco closeup by Alfredo Matacotta, via; broccoli Romanesco on a plate by Dror Bar-Natan; cartoon, originally published in the New Yorker magazine in 1928, by Carl Rose (illustrator) and E.B. White (writer) via CartoonBank. All fractals made by the author using ChaosPro.


  1. #1 cleek
    November 27, 2006

    here’s a shot i took of the inside of a Romanesco broccoli:


    they’re fractals on the insides, too.

  2. #2 Kim Boone
    December 5, 2006

    Actually, I always loved broccoli, even as a small child. Maybe it has something to do with the fact that my father grew it in the garden, and it never took longer than an hour to get it from the land to the plate.

    Hi there! It’s been way too long, I know. My friggin’ computer totally gave up on me some months ago, and now I only get sporadic access to the internets until I can get my hands on some serious cash (nothing illegal ofcourse). Good to see you’re still going strong.

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