An interactive fractal exhibit

[William Beaty <billb@eskimo.com>]

On Thu, 18 Apr 1996, Bob Hunt wrote:

> I have been contacted by a local science museum that wants to set up a
> display showing "chaos," ideally with interactive components for children.
> Any ideas?

Something I came up with to add interactivity to the travelling exhibit on
fractal art while it was at MOS in Boston: video fractals

Around 1984 while I was messing with video feedback, I chanced to place a
mirror in the optical path and was rewarded by all kinds of strange
treelike patterns.  By tilting the camera I could create objects
resembling river networks, kidneys, sectioned broccoli, etc.  Messing with
the color-balance controls caused strange nonrepetetive flashes and waves
of color.  Mildly amusing, but then within a couple of years the whole
Nonlinear Dynamics field caught fire, so I was prepared. 

Feed the video output of a color camera to a large monitor screen.  Obtain
a fair-sized glass mirror with one dimension being about 1ft, the other
being the same as the vertical dimension of the monitor screen.  (I used
two 12" mirror tiles glued to a board.)  Place camera and mirror as shown
below (if viewed from above): 
               __________________
               |                |
               |                |   VIDEO
               |                |  MONITOR
               |                |
               |_--------------_|
                             |
                             |
                             |  MIRROR
                             |
                             |


                 ___
               _/  /_
              /    /
             /    /  CAMERA
            /    /
           /____/


Point the camera at the edge of the mirror where it touches the monitor
screen, and adjust zoom and monitor brightness to produce a bit of
feedback.  You'll see patterns which look like a 12" ruler, with larger
vertical tick marks divided by smaller ones.  Try waving your hand across
the screen.  Zoom in a bit, and you'll produce a dynamic effect resembling
the view from a speedboat pushing its way through a field of reeds.

Now, *twist* the camera so it views the same point from a tilted angle. 
The straight line on the screen will bend, and its ends will swirl into a
bilateral symmetrical pair of vortices, and the entire line will break up
into smaller copies of these swirls. 

          ___----------___
        /  __        __   \     THE OVERALL PATTERN
       |  /   \     /   \  |    (without the iterative
        \____/  | |  \____/      subdividing effect)
               /   \


The pattern resembles a broad fan of tree-roots.  It is composed of
"infinite tunnels" which are normal for video-feedback effects, but the
mirror successively divides the tunnels into two, four eight, etc., to
create an infinite fan of infinite tunnels.  The camera tilt causes each
successive deeper iteration to appear rotated either CW or CCW,
and the entire affair spreads off to infinity along the curved upper
border.

   Change the camera zoom and you directly change the fractal dimension.

   Change the tint control on the monitor, and the pattern aquires 
   the color banding typical of Mandelbrot/Julia set mappings.

   Place your hand upon the monitor screen and the video fractal
   changes its nature: it becomes composed of an infinite number
   of fingers!

To produce a robust exhibit I placed the video camera above the monitor
and folded the optical path with more mirrors, then enclosed the whole
thing inside a case.  I provided a big slot which allowed museum visitors
to place hands, coins, etc. in the path.  Two buttons were provided to
alter the zoom.  I didn't have time to bring the tint-control from the
monitor out to a knob. 

The system is a massively-parallel optical processor which produces 2-D
affine transforms at a 16mSec clock rate.  (a good intro for a lecture,
followed by your unveiling a simple TV camera?)  The mirror produces the
nonlinearity, and the tilt of the camera changes the equation which
generates the fractal.  Without distortion, the system produces fractals
based on Affine transformations (rotation and translation between
iterations.) 

I later realized that with judicious use of properly distorted plastic
mirrors, my fractal system could have produced genuine Julia sets.  A
Julia set requires a mirror which produces n^2 distortion.  A
stretched-mylar mirror bent by probing fingers would probably would come
close.

Someone at the Ontario Science Center built a system which came close to
Julia Sets by including a second mirror which then generated patterns like
this: 

          ___----------___
        /  __        __   \
       |  /   \     /   \  |
        \____/  | |  \____/
            __ /   \ __
         ____  \   /  ____
        /    \  | |  /    \
       |  \ __/     \__ /  |
        \ ___          ___/
             ----------

Another thing I didn't have time to pursue: small mirror chips placed in
front of the monitor and tilted to reflect parts of the monitor screen
back to the camera.  This technique should be able to generate the classic
"fern" fractals, and possibly many other biological forms resembling
leaves. 

......................uuuu / oo \ uuuu........,.............................
William Beaty  voice:206-781-3320   bbs:206-789-0775    cserv:71241,3623
EE/Programmer/Science exhibit designer        http://www.eskimo.com/~billb/
Seattle, WA 98117  billb@eskimo.com           SCIENCE HOBBYIST web page