2.32 Martin Attractors
(type=hopalong/martin)
These fractal types are from A. K. Dewdney's "Computer Recreations"
column in "Scientific American". They are attributed to Barry Martin of
Aston University in Birmingham, England.
Hopalong is an "orbit" type fractal like lorenz. The image is obtained
by iterating this formula after setting z(0) = y(0) = 0:
x(n+1) = y(n) - sign(x(n))*sqrt(abs(b*x(n)-c))
y(n+1) = a - x(n)
Parameters are a, b, and c. The function "sign()" returns 1 if the
argument is positive, -1 if argument is negative.
This fractal continues to develop in surprising ways after many
iterations.
Another Martin fractal is simpler. The iterated formula is:
x(n+1) = y(n) - sin(x(n))
y(n+1) = a - x(n)
The parameter is "a". Try values near the number pi.
Michael Peters has based the HOP program on variations of these Martin
types. You will find three of these here: chip, quadruptwo, and
threeply.