Fractal Landscape spreadsheet

Here is a Microsoft Excel^tm spreadsheet that generates surfaces that look like fractal landscapes. They are generated along the same general lines, although the process is not rigorously fractal (the structure has a very limited scale of self-similarity) nor very efficient (as it is meant to be easy to understand, and because frankly this is a doodle I did during a long train ride)

Here is the approach.


I take an initial grid, and fill it with random 'peaks'>

Then I take each of the 'squares' in the grid and split it into four like this:

Then I smooth the edges by making each cell in a new graph the average of 9 cells in the old one, like this

And then I add another random factor to each cell. The random numbers are K times as big as the original ones, as otherwise the 'noise' would swamp the underlying pattern you are building up. K<1

Then you start feed the 4x4 array back into step 2, and do it again, then a 16x16 array and so on. In practice, you 'loose' a bit of edge each time, as you cannot average properly otherwise in step 3. In the spreadsheet, steps 3 and 4 are carried out at the same time.

At the end, you make any 'height' below a certain level = 0, and that is sea level. So there are two basic variables:

'erosion' - in fact, 1/K. if =1 you just get a lot of spikes. 1.7 - 2 gives rocky Cornish coasts, 4-5 gives smooth Scottish hills.

'sea level' - which is obvious.

The 60x60 spreadsheet does exactly that, generating a 60x60 grid (3600 height points). As it uses the Excel^tm inbuilt random number generator, every time you alter anything in the sheet it recalculates a completely different landscape.

The 30x120 landscape looks more realistic for three reasons. I have biassed the height of the row of initial points nearest the viewer to be low, so that the view does not often end up inside a mountain. I have made the array longer than it is deep, so it looks more like a view through a window. I have altered the colours on the plot so they sort-of match landscape colours. And I have added an additional fudge factor 'steepness', which is the power to which the final heights are raised before plotting. This means that sea-level slopes are more gradual than mountain ones.

Here are the files, suitably compressed for windows and Mac. Both spreadsheets are big - about 500kbytes.

Here are four sample landscapes generated with 30x120.

Have fun.