LANDSCAPE 0.5-SNAPSHOT

Fractal Landscape Generator
Written in Java by @grkvlt.

This project was inspired by lockdown conversations with my friend B about maths and science; during which I realised I had known about the technique for twenty plus years but had never attempted to implement it. I developed an initial rough working system in just a few hours of hacking, and was very pleasantly surprised at the quality of output from such a simple algorithm and rendering technique.

$fractal landscape banner$

After further modifications to produce images suitable for Twitter I also showed B the progress so far. After a bit of live coding to show them how the program worked, they suggested adding some kind of smoothing mechanism to create more natural looking plains. I implemented our ideas as a low-pass filter based on the gradient, described below.

I am really happy with this project! The ratio of coding effort to aesthetically pleasing pictures has been incredibly high so far, and I intend to keep playing with the code and adding more features. Future plans include implementing a more sophisticated renderer with perspective, and displaying the output as a real-time fly-through of the landscape...

Usage

The program requires at least Java 8 with a Maven installation. It has been optimised for use with OSX, but this is not essential. The Jar file created can be executed without any other dependencies, using the JRE java command.

Program arguments are optional, and are used to set configuration for:

Roughness value
Number of images to generate
Image file prefix

Example

$ mvn clean install
[INFO] Scanning for projects...
[INFO] 
[INFO] ------------< landscape:landscape >------------
[INFO] Building Landscape 0.5-SNAPSHOT
...
$ java -jar ./target/landscape-0.5-SNAPSHOT.jar 2.174
+ Fractal landscape generator - Landscape 0.5-SNAPSHOT
+ Copyright 2020-2022 by Andrew Donald Kennedy
- Using 2.174 roughness and water 0.125
- Generating landscape over 6 iterations
...

Algorithm

The code uses the diamond-square algorithm 1 for random midpoint displacement to generate a height map representing the landscape. The slope of each point is determined using a simplified approximation of the vector calculus gradient operator. A low-pass filter is applied wherever the gradient is less than some threshold, by averaging the points height with its neighbours, to produce smoother surfaces.

The image is rendered in (pseudo) 3D by drawing a sequence of line segments along the x-axis from left to right, with the y-axis showing the height. Hidden surface removal is achieved simply due to the order of operations and treating the line segments as the border of a filled polygon. Finally some x-axis jitter is added to attempt to alleviate the artifacts at cell boundaries that occur with this algorithm.

Code

An outline of the code flow is shown below; the variables used are as defined in the Images.java 2 file.

// Generate height map
double[][] points = landscape.generate(r, w, h);

// Differentiate height map
double[][] grad = landscape.differentiate(points);

// Smooth height map
double[][] smooth = landscape.smooth(points, grad, t, fi);

// Render and save image
BufferedImage image = landscape.render(smooth, scale, water, z, b);
String file = save(image, "PNG", ".", "landscape");

References

The book The Science of Fractal Images is an excellent text on fractals, and was where I first learned about techniques for the generation of realistic fractal landscapes using brownian 1/f noise. The papers listed in the Wikipedia article on the Diamond-Square Algorithm are also useful, and searching for this or Midpoint Displacement should result in many blog posts and articles suitable for providing further inspiration.