A GPU-accelerated Julia set visualizer, using Vulkan!

Interactively generates Julia set visualizations for complex polynomials of the form f(x) = x^n + c.

Written in Rust (and some GLSL). You will need Vulkan development headers in order to compile, but there shouldn't be any other non-Rust dependencies. Build with

cargo build

and run with

cargo run

Command-line options

No command-line options are required, and all of their parameters can be changed interactively. The default settings bring up the Julia set for f(x) = x^2, i.e. a unit circle, visualized with a black background and a white foreground.

• --exponent <integer> or -n <integer> -- The n in x^n + c. Default is 2.

• --real-part <float> or -r <float> -- The real part of the constant c in x^n + c. Default is 0.

• --imaginary-part <float> or -i <float> -- The imaginary part of the constant c in x^n + c. Default is 0.

• --center <complex> or -O <complex> -- The complex number at the center of the image. <complex> is a comma-separated list of exactly two floating point values. Default is 0.0,0.0.

• --extents <float> or -e <float> -- The extent on the complex plane covered by the largest image dimension. (This is essentially zoom; smaller numbers zoom in closer.) Default it 3.6.

• --iters <integer> or -m <integer> -- The number of iterations per point in the visualization generation. Default is 100.

• --width <integer> or -w <integer> -- The width in pixels of the interactive image. Default is 800.

• --height <integer> or -h <integer> -- The height in pixels of the interactive image. Default is 800.

• --colors <colors> or -c <colors> -- The colors for the visualization. <colors> is a comma-separated list of at least two and at most three color specifications, which may be either named colors from the CSS3 specification, or hex codes of the form #aabbcc. The third color, if absent, defaults to white. Default is black,white.

• --midpts <midpoints> or -g <midpoints> -- The gradient points for the visualization. <midpoints> is a comma-separated list of at least one and at most three values between 0.0 and 1.0, and are interpretted as follows:

  • If only one value is given, it is the gradient point of the second color. The first and third colors default to gradient points 0.0 and 1.0 respectively.
  • If two values are given, they are the gradient points of the first and second colors respectively. The third color defaults to gradient point 1.0.
  • If three values are given, they are the gradient points of the three colors respectively.

  Default is 0.5.

Interactive interface

When julia starts up, it will display a window containing the visualization. If it was not started from the command line, it should also open a command line window, since that's where all of the non-visual components of the interface live. Controls are (almost) entirely keyboard-based. It's a very janky interface.

To pan the viewport around the complex plane, simply click and drag in the viewing window. You can also use WASD to move the viewport, (hold Shift to make smaller steps). To zoom in and out, either scroll in the viewing window with the mouse wheel, or use the keyboard Plus and Minus keys.

To re-center the image, press C. To reset the zoom, press Z.

To change the polynomial c, use the arrow keys. Up and down will change the imaginary part, while left and right will change the real part. Holding Ctrl will make c take bigger steps, Alt will make it take smaller steps, and Shift will make it take even smaller steps; Alt+Shift will make it take the smallest steps of all.

To change the exponent n, use PageUp and PageDown.

To change the iteration count of the visualization, use the left and right square bracket keys; [ will decrease the iterations, and ] will increase them. More iterations yield higher detail in the generated image, but might also make your computer rebel against you for torture, so tread lightly.

To export a PNG of the current visualization, press E. The file name will be auto-generated based on the current parameters of the visualization. To increase and decrease the export resolution width, press I and K respectively. To do the same for the export resolution height, press O and L.

To modify the visualization gradient, notice that a particular color code and gradient point are enclosed in [square brackets] in the text interface. These are the current active color and gradient point. To set the active color, use the number keys 1, 2, and 3. To set the active gradient point, use 4, 5, and 6.

To change the active color's hue, use the R and F keys. To change its saturation, use T and G. To change its value, use Y and H.

To modify the active gradient point, use U and J.

To exit, either close the viewing window, or press Q or Esc.