In each animation r is initalized to a number rmin < 1, incremented by dr = .0003 until r = rmax > 1. If you choose close-up (by clicking in the box labeled "close-up"), rmin = .985 and rmax = 1.0125, if you choose normal, rmin = .99 and rmax = 1.4. (Default is normal.) For each r, 400 points in the orbit of 0 are plotted using the function

f(z) = z^2 + c

where c = (r*e^(i*2*pi*alpha))/2 - (r^2*e^(i*4*pi*alpha)/4)

By clicking in the appropriate box you may choose one of 4 ways to increment alpha:

Rational: alpha takes on the values 1/2, 1/3, 1/4, 1/5, ...

Irrational: alpha starts at 0.1437120163 increases by increments of .0031415926

Random: alpha is chosen at random from the interval [0,1]

"Almost rational": alpha takes on the values 1/2 +.001, 1/3 +.001, 1/4 + .001, ...