
Martin Attractors

formulas: 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.

