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Diamond Square Terrain Generation

Here’s an interesting little algorithm I coded up before an interview – Terrain generation with the Diamond-Square Algorithm.

The algorithm itself is quite simple, but makes some nice graphs.


Initialize the corners of your N*N area randomly. Square Section – Get the center point of your corners and set it to be the average of those 4 corners ± a random amount Diamond Section – Get the center of each edge and set itto be the average of the surrounding diamond shape ± a random amount In the example image, the left red point would be the average of the black points above, below and to the right of it – but you should include a fourth point if it exists. Repeat until your grid is populated.

Here’s what this looks like with a simple heat map in 2D:

And in 3D:

This is a very simple algorithm to implement, but quite effective for what it does. You can change the random variant to increase the choppiness/smoothness of the resultant graph. The more points in the grid, the better this looks. Take this high-N example from playful.js for example:


Setting the sea level in your render is a matter of picking a Y-level and wherever there isn’t any rock below this point, fill the area with water. This is a pretty nice way to get both lakes and hills in one step.

There’s also an added benefit of exporting the co-ordinates so you only have to ever compute the terrain once.

You can browse the source of my implementation (In Python 2.7) on my Github

This post is licensed under CC BY 4.0 by the author.