Decomp Method

© by Jay Hill, 1998.

Here is my interpretation of what we mean by decomp. The algorithm in C++ is

int ColorPoint(Complex c){
// Decomp (c) by Jay Hill 1998
int color=0;
Complex z=0;
for(long int k=Maxiter; k>0; --k, z=z*z+c)
if(norm(z)>1048576.)
return real(z)>0?RED:LIGHTCYAN;
return color;
}

An MSDOS program, with some enhancements for early detection of period 1, 2 and 3 components, plots the image like this, Figure 1:

Figure 1. Decomp image.

To run the Decomp program, unzip the Decomp.zip file and type Decomp. You will see minimal instructions:

Decomp [Skip] [Xcenter] [Ycenter] [Xwidth] [Maxiter] Defaults: int Skip=1 double Xcenter=-.75 double Ycenter=0 double Xwidth=4. long Maxiter=256

Skip tells the program to skip plotting some pixels (for quick looks). Skip=1 does ever pixel, skip=2 does ever other pixel, etc. Run it the first time with

Decomp 1

and see the Figure 1. Then try

Decomp 1 -1.75 0 .2

and see Figure 2.

Figure 2. Decomp centered at -1.75.

And then you can use this to see the period 4 midget:

Decomp 1 -.1589 1.0319 .16