Loaves & Fishes 27

Shape produced by the Mandelbrot set
is always positive, and a positive
number squared is also positive.
So real numbers are only the
square root of positive numbers.
But imaginary numbers are not
positive, they’re not negative,
and they’re not zero. On a number
line, positive numbers are to
the right of zero, and negative
numbers are on the left. We can
add a vertical axis to the number
line for the imaginary numbers.
Complex numbers
consist of a real number
component and
an imaginary number
multiplied together.
The Mandelbrot
Set is all of the complex
numbers that
run through the formula
above and never
get far away from 0.
These complex numbers
are then plotted,
on a two dimensional
chart, not
just a number
line. Numbers
that are part of
the set are black.
Numbers that are
almost part of the
set are assigned
other colors, depending
on how
quickly Z climbs
away from zero.
Turned into a picture, this
short little formula, Z = Z 2 + C,
produces an incredibly complex
shape. In fact, it is infinitely
complex, as complex as anything
can be. As you zoom in on this
shape, you see that is it very selfsimilar.
That little black spot to
the left of the image is a “baby”
copy of the original image. And
the little black spot to the left of
that one is another baby copy.
Infinite detail emerges as you zoom in.
Loaves & Fishes • Issue 27 | 13