Fractals

Fractal image generation

This example illustrates how to generate images of different types of fractals and save them to disk. All key parameters can be specified at the command line, to produce a variety of calculations and views.

Internally, calculations are performed using the Tensor type, allowing for efficient parallel computation. Both eager-mode and X10 backends are supported, demonstrating how to perform parallel calculations on the CPU or various accelerators.

Generating the Mandelbrot set

To calculate an image of the Mandelbrot set with default parameters, you can simply run

swift run -c release Fractals MandelbrotSet

This will save out a resulting image in the local file mandelbrot.jpg that will look something like the following:

A number of parameters can be customized at the command line to look at different regions of the fractal, or otherwise change how it is calculated or rendered. Here's an example that explicitly specifies all the parameters, and has the calculation run via XLA on the default accelerator using the X10 backend:

swift run -c release Fractals MandelbrotSet --iterations 200 --tolerance 4.0 \
  --region=-2.0,1.0,-1.3,1.3 --image-size 256,256 --x10 --output-file mandelbrot 

The relevant parameters are:

• iterations: The number of iterations of the Z * Z + X calculation to perform.
• tolerance: The threshold for which divergence of the calculation is determined.
• region: A comma-separated list corresponding to the region real_minimum, real_maximum, imaginary_minimum, imaginary_maximum. Note: if the region starts with a negative number, an equals sign is needed between the argument name and the region value.
• image-size: The size of the resulting image, specified as the comma-separated pair width, height.
• x10 or eager: Whether to use the eager-mode backend (default) or the X10 backend for the calculations.
• output-file: The base name of the image file to write out.

Generating the Julia set

swift run -c release Fractals JuliaSet

This will save out a resulting image in the local file julia.jpg that will look something like the following:

As with the Mandelbrot set above, many relevant parameters for creating an image of the Julia set can be specified at the command line. Here's an example that explicitly specifies all the parameters, and has the calculation run via XLA on the default accelerator using the X10 backend:

swift run -c release Fractals JuliaSet --constant=-0.8,0.156 --iterations 200 --tolerance 4.0 \
  --region=-1.7,1.7,-1.7,1.7 --image-size 256,256 --x10 --output-file julia 

The relevant parameters are:

• constant: The constant C, specified as a comma-separated pair of real, imaginary.
• iterations: The number of iterations of the Z * Z + C calculation to perform.
• tolerance: The threshold for which divergence of the calculation is determined.
• region: A comma-separated list corresponding to the region real_minimum, real_maximum, imaginary_minimum, imaginary_maximum. Note: if the region starts with a negative number, an equals sign is needed between the argument name and the region value.
• image-size: The size of the resulting image, specified as the comma-separated pair width, height.
• x10 or eager: Whether to use the eager-mode backend (default) or the X10 backend for the calculations.
• output-file: The base name of the image file to write out.