To use, enter the following command into the command line: raco pkg install domain-coloring. Once the package has been installed, you can access it either in DrRacket or in the racket run-time system by typing (require domain-coloring)
If you would rather download the github files, you can do the following:
Open DrRacket and run the complex-grapher-test.rkt file in the same folder as complex-grapher.rkt. This program requires you to install the colors package, which you can do from the command line with raco pkg install colors.
You can also run the complex equation grapher in the racket run-time system:
- See your current directory with
,pwd - Navigate to the containing folder with
,cd <path> - Run the command
,enter "complex-grapher-test.rkt"
The following commands may be used to control the calculator:
(help) : show this dialogue
(graph eq) : graph the complex-valued procedure eq
(graph eq scale) : graph with scale being the horizontal span of the window in units
(graph eq scale x y): graph with x and y being the real and imaginary offsets from the origin
(set-res res) : set the resolution to the given number of pixels (lower values draw more points)
(show) : show the window and canvas
(hide) : hide the window and canvas
(reset) : reset the canvas to default
(mandelbrot) : draw the mandelbrot set
(polynomial . coefficients) : create a polynomial procedure
(zero-pole m n) : create a function with m zeroes and n poles
(complex x y) : create the complex number x+yi
(random-complex) : create a random complex number in the unit square
(f: args ~ form) : define a formula
(>> arg . procs) : pipeline arg through procs left to right
The window can be manually resized by dragging the border and the calculator will automatically update.
Left clicking anywhere on the window will cause the calculator to zoom in to double the magnification and recenter the graph at the clicked point.
Right clicking the window will cause the calculator to zoom out to half the magnification and recenter the graph at the clicked point.
Additional explanation and details on implementation can be found in the comments in the source files.
The default equation shown by (reset) is the identity function. This shows a one-to-one correspondance between inputs and outputs.
The position on the canvas serves as the input. Horizontal displacement correspond to the real axis with positive numbers to the right.
Vertical displacement corresponds to the imaginary axis with positive multiples of i to the bottom.
The output for a given point is represented by the color at that point. The magnitude of the output corresponds to lightness: the darker, the closer to zero, and the lighter, the closer to infinity. The hue represents the angle of the output: red is positive real, cyan is negative real, indigo is positive imaginary, chartreuse is negative imaginary, etc.
Zeroes in the output appear as completely black, whereas poles (a.k.a. 'infinite discontinuities') appear as completely white. The default window settings place the origin in the very center of the screen, with the horizontal and vertical window spans each being 4 units across.