Click on the green flag and run in Turbo. I chose to plot in white on black so as to focus on the mathematics. Other Hopalong projects use color but my taste is to not add color to equations. Also, I chose to require the user to 'See inside' to change the variables a, b, c and the magnification so as to keep the screen clear. The variable m is used to save the value of x for use in the y equation to complete the iteration cycle. X is then set to m to start the next iteration. The variables are currently set to a = 0.4, b = 1, c = 0, and magnification set to 130.
According to Dr. Martin he was exploring the Henon Attractor (see http://scratch.mit.edu/projects/10875942/) and he started playing with the equations and hit upon this pair that creates 'Hopalong'. x= y - SGN(x) * √(ABS(b*x - c)) y = a – x If x < 0 then SGN is set to -1 else x is set to +1. Try these values for the variables a/b/c/magnification 0.5/-0.6/0.7/6 -0.5/0.5/0.7/25 -0.25/-0.6/-1.7/6 33/0.34/0.55/10 -0.25/-0.643/-3/10 555/1111/555/1 -11/0.05/-0.5/20
