
Lambda Sets

formulas: lambda


This type calculates the Julia set of the formula lambda*Z*(1-Z). That is,
the value Z[0] is initialized with the value corresponding to each pixel
position, and the formula iterated. The pixel is colored according to the
iteration when the sum of the squares of the real and imaginary parts
exceeds 4.

Two parameters, the real and imaginary parts of lambda, are required. Try
0 and 1 to see the classical fractal "dragon". Then try 0.2 and 1 for a
lot more detail to zoom in on.

It turns out that all quadratic Julia-type sets can be calculated using
just the formula z^2+c (the "classic" Julia"), so that this type is
redundant, but we include it for reason of it's prominence in the history
of fractals.

