Complex Domain Coloring using fztopng  

fztopng is a SLang script that converts a function of a complex number over a region of the complex plane into a PNG image. The script requires at least version 2.1.0 of the SLang library, as well as PNG support. The script may be downloaded from this link. Running the script without any arguments will produce a usage message: Version 0.1.0 Usage: ./fztopng [options] f func  func.sl Options: xreal xlo:xhi:#N Grid for x=Real(z) (default: 2:2:#512) yimag ylo:yhi:#N Grid for y=Imag(z) (default: 2:2:#512) iter N Iterate N type (default=1) hsv Use HSV method (default) hue=float,float Min/Max values of Hue ([0>360]) sat=float,float Min/Max values of Saturation ([0>1]) val=float,float Min/Max values of Value ([0>1]) grad Use gradient method rgb=int,int Min/Max RGB values for gradient method o file.png Output file (default: func.png) hhelp This message Note: The file func.sl must contain a function called f_of_z. If the f expr form is used, it must involve z, e.g., f sin(z) As the usage message shows, the script implements two methods for associating a color with a complex number: the HSV method and the Gradient method. The HSV method maps the phase and modulus of the complex number into the color's HSV representation using:
The above equations indicate that S and V lie in the range 0
to 1, whereas H is an angle that runs between 0 and 360 degrees. The
fztopng hue=240,270 myfunc.slwould produce a "blueish" image with the hue lying between 240 and 270 degrees.
In contrast the Gradient method uses the phase of the complex number
to linearly interpolate between two colors in the RGB
representation. It does not use the modulus at all. The two RGB
values may be specified using the fztopng grad rgb=0xFF0000,0x00FFFF myfunc.slIn this example, as the hue increases from 0 to 360 degrees, the red component decreases from 255 (0xFF) to 0, while at the same time the green and blue components increase from 0 to 255 (0xFF).
The
Unless specified by the fztopng myfunc.slwill produce a PNG file called myfunc.png .
There are two ways of specifying the function: via a file containing a
SLang function called fztopng x 8:8:#512 y 2:2:#128 o sin_hsv.png f "sin(z)"This produces a PNG file called sin_hsv.png containing the 512
by 128 pixel image:
The most flexibility is achieved using a file coded in SLang
containing the function called 
This page was last updated Jan 5, 2014 by John E. Davis. To comment on it or the material presented here, send email to jed at jedsoft org.