This program generates Newton Basins for functions F(t, z) for real t between 0 and 1 and complex z, defined as:
F(t, z) = G(z) + t(H(z) - G(z))
and allows the user to animate the results. In its current state the program presents prompts for several variables before it actually starts generating the animation. The user is required to type in expressions for the real and imaginary parts of the two functions G and H and their derivatives. The expressions are evaluated with Sadao Massago's evallt routines. If you know how it would be wise to comment out the expression evaluation calls in the functions U, V, W, Z, T, S, Q, and R in NewtonAnimator.c, and replace them with the functions that you want to use. The evallt calls are nice if you don't want to poke around in the source code but they take a long time. If you don't want to type responses to prompts you can cause the program to take the responses from a plain text file by typing:
./Newton-Function-Animator < [path]
where the file pointed to by [path] is a plain text, white space delimited list of answers to the prompts in the order that they appear. Below are some screen shots from Newton-Function-Animator and a download link for the source code.
 |
 |
 |
 |
 |
 |
 |
 |
 |