## Cauliflower

One of the properties of fractals is that they contain no
information that gives you a
sense of scale: little pieces of a fractal look like the
whole thing, and in particular, if someone
shows you a zoom in to a fractal,
you can't tell if they've zoomed in by a factor of 10 or
10 * million*! Now, Nature's best fractals have this "detail
in the detail" property for only a finite number of repetitions,
and the cauliflower is one of the best examples. Its surface is
made of big bumps. On the big bumps are smaller bumps, and on those,
still smaller bumps, and so on. It's easy to visualize each big
bump as a whole cauliflower in its own right. Indeed, although the
right-hand picture is a zoom into the one on the left, it's not too
hard to imagine that you are looking at a whole pile of cauliflowers
on display at your local supermarket.

## Side View

Below on the left is a cut right through a cauliflower. And a fractal
structure appears. But wait! Actually this is just one piece of a
cauliflower; can you find where it appears in the cross-section
of a whole (really!) cauliflower on the right?

## The Cauliflower Family

Yes, there's the big daddy on the right, smaller
mom on the left and the little kids in front --- looks like four
different sized cauliflowers, right? But these are
all pieces of the same single cauliflower. The
point is, when you break off a piece of a fractal, it looks again like the
whole fractal, just smaller.

** Details: ** I produced these pictures for the
Science and Math Academies for Maine K-12 teachers
(more about the Academies can
be found at other places in this document).
For teachers who are interested in teaching fractals to
their students, I wanted to emphasize (1) that fractals are
found all around us, and (2) it's possible to create displays
about them without expensive materials.
Using a 35mm camera on a tripod,
I took these pictures for the "slide show" portion
of my week with the Academy teachers.
Arranged on dark blue construction paper, the
cauliflower was photographed using incandescant lighting,
and a blue filter to compensate for excess amount of red light
produced by regular household lightbulbs...