A simple library for generating fractals.
It's difficult to pin down a single, authoritative definition of exactly what a fractal is. Self-similarity - though not necessarily repetition - seems to be a central component. We've all seen images of fractals, whether it's a Sierpiński Triangle or the famous Mandelbrot set, either in movies or popular science media.
The primary focus of this library as it currently stands is the production of images generated by repeatedly applying a function to a point in the complex plane. This includes Julia sets and, by extension, the Mandelbrot set. There is also work being done to include a class of generative methods developed by Kalantari and others which have been grouped under the name polynomiography.
To work with gofrac, you can use Go's package manager to install it by issuing the following command:
go get github.com/cfdwalrus/gofracAdditionally, you'll need Lucas Beyer's go-colorful package, which can be found here.
Having installed the requisite packages, you can use gofrac in your project simply by including it with an import statement:
import "github.com/cfdwalrus/gofrac"For a quick start, see the examples in gofrac_examples.go.
The library has a modular design in which the selection of components determines the output. These components are the class of fractal to be rendered, the domain in which it is to be calculated, the selection and manipulation of resultant quantities for plotting, and a palette consisting of a set of colors coupled with a method by which they are chosen.
For example, in order to produce the classic image of the Mandelbrot set, one would choose the appropriate components. (N.B.: Other classes of fractals are available in the library, and you are free to create your own!)
The first step is to choose a class of fractal. The Mandelbrot struct implements the complex quadratic equation used to produce it, so we would create an instance of it with an appropriate escape radius - say, 80.0.
m := gofrac.NewMandelbrot(80.0)With that determined, the next choice is which points in the complex plane should be rendered. The majority of the Mandelbrot set lies in the rectangle spanned by the points (-2.5, -1.0) and (1.0, 1.0), where the point (a, b) represents a complex number a + bi. Setting the number of samples to be taken along each axis of the bounded area allows gofrac to calculate the points at which it should iteratively apply the Mandelbrot map.
w := 1280
h := 768
d, err := gofrac.NewDomain(-2.5, -1.0, 1.0, 1.0, w, h)It's time to choose which part(s) of the output are important. For our example, that is the escape time, i.e. how many iterations it took for the modulus of the iterate to exceed the escape radius chosen earlier. Since this happens almost immediately away from the boudary of the set, normalizing the escape times will perhaps yield a more visually interesting result.
plot := gofrac.NormalizedEscapeTimePlotter{}In order to visualize the values produced by the plotter, gofrac uses a color palette. For the purposes of this library, a palette is anything that takes a floating-point value and the maximum number of iterations to be performed before considering a value to have converged. There are several such palettes defined in palette.go to choose from, as well as more concrete examples in palette_example.go.
pal := gofrac.SpectralPalette{Sweep: 270, Offset: 0}The final parameter to choose is the maximum number of iterations to perform before an unescaped point is considered to converge. Tuning this parameter will increase both the level detail in the resulting image as well as the time needed to produce it.
maxIt := 250With everything chosen, the only thing left to do is to tell gofrac to create an image for you. The GetImage function does exactly that. Using the objects defined above, one issues the call
img, err := gofrac.GetImage(m, d, &plot, pal, maxIt)GetImage returns an *image.RGBA, which the standard library's various encoders can use to write an encoded image to disk. Consult the documentation of Go's image package for details.
After doing so, you should have the following image of the Mandelbrot set in your filesystem. Way to go!
The GetImage function provides a convenient interface to generate images of fractals in a one-off manner but precludes the reuse of results for multiple rendering runs. The FracIt function will return a two-dimensional slice of object containing the output quantities of the iterations. This slice can then be passed to the Render function with different plotters and palettes depending on your needs.
Copyright (c) 2020, Andrew Quinn
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