Jason
Padgett discovered how fractals arise from relativity
and limits. He is a geometric mathematical savant and
lives in Washington state where he currently studies.

This
is a hand drawn fractal of the structure of space time
at the quantum level (Planck length/Planck Particle
size frame). It shows a time lapse film of a mathematical
savant, Jason Padgett, hand draw the fractal. Color
was added by computer
and wave equations make his drawing vibrate. The
equation describes the geometric connection between the
quantum
energy (very small,
hw) and the the energy described by Einstein's famous
E=mc^2.

How
to Make a Fractal
By Hand

Step
1: Draw an outline of the shape you want to draw a fractal
of. In this example we will use a pentagon
that is sliced into 40 equal segments. To make the pentagon
perfect you must first draw a circle with a compass.
Now
that you have the circle drawn you divide 360 degrees
by 40 and
you get nine degrees. Now, you must take a 360 protractor
and put its center at the center of the pentagon. (The
center of
the pentagon is the center of the initial circle. Just
look for the small 'hole' made in the paper by the compass
to find
the center of the pentagon). Now take a small piece of
tape and use it to tape the compass in place so it will
not move
as you measure the angles. Now use a mechanical pencil
(3mm to 5mm pencil lead works best)to make a small dot
every 9 degrees.

In
other words, draw a straight line from 0/360 degrees
to 180. From 9 degrees to 189, 18 to 198 and keep doing
this until
the pentagon is sliced into 40, nine degree segments.

Note
that you are NOT slicing the circle into forty segments,
just the pentagon. We just drew the circle at the beginning
to make drawing a perfect pentagon easier. So when
you are slicing the pentagon into segments you stop the
lines
that
you are drawing when you reach the perimeter of the
pentagon.

So
at this point what we have is a pentagon sliced into 40
equal segments. Now we are
going to turn this
shape
into 40
right triangles (I use right triangles because that
is how energy travels, magnetism, radar, etc.)

To
do this you draw a straight line from 0/360 degrees (at
the perimeter of the pentagon) to ninety degrees.
This makes
a 45, 45, 90 degree right triangle that goes from
0/360 to the center to 90 degrees and back to 0/360.
Now
draw a straight
line from 9 degrees to 99 (remember that this line
starts and ends on the perimeter of the pentagon).
Then draw
a straight
line from 18 degrees to 108, 27 to 117, 36 to 126
etc...until you have connected all of the triangles.

At
this point the fractal looks like this. (See picture of
one hexagon sliced into 40 right triangle).

Now
what we are going to do is translate the entire shape (the
entire pentagon). Remembering back
to algebra we
learned that
you can graph any equation. So if you take
a basic function say f(x)= 2x + 1 and graph it you translate
the points
onto a graph and make a line. If x=0 then y=1,
if x=1 then y=3 etc.
We are doing the same thing with fractals only
we are translating the ENTIRE SHAPE instead
of
just
a point.

Take
your compass and make sure that it is set to make the exact
same size circle
that
we started
with
when
we made the
first pentagon. Now put the compass right
on the tip of the first 'peak' of the pentagon
(the first
peak
is touching the
perimeter of the first circle at 0/360 degrees).
Then draw another circle (it will be the
exact same size
as the first
circle). Now repeat the process of using
this circle to make a pentagon. Then slice the pentagon
into
40, nine degrees segments.
Then connect the segments into right triangles
just like the first.

Now
repeat this process only put the center of each new pentagon
on the
points of the
original pentagon
that
are touching the
original circle's perimeter. And there
you have
it, a fractal drawn from right triangles.

This
is a basic version of how to draw a fractal of anything.
You can change it up by slicing any shape into right triangles
or any other type of triangle. Or if you want to give the
appearance of depth/motion you can draw the initial pentagon
(or whatever shape your using) and then when you draw the
other five pentagons (or whatever shape your using) make
them all smaller (by the same factor) or make them larger
(by the same factor).