Mastering Nature's Patterns: Basalt Formations

I love patterns. This all originally stems from my observations of nature's patterns. A lot of the objects I draw (and develop in code mathematically) come directly from nature.

Strikingly, nature will often conspire to produce objects of great beauty, ones which we cannot match without tremendous effort. An example of this are the basalt formations. Created by volcanic upwelling, great pressure leading to crystallization, and fracturing during cooling, they are nature's brilliant tessellations, awe-inspiring extrusions, and mad ravings simultaneously.

They resemble three-dimensional bar graphs. Their fracture pattern, in two dimensions, is a natural Voronoi diagram. I first saw this pattern in nature while observing the way that soap bubbles join. Without fully understanding it, this observation introduced me to the mathematical laws of geometry when I was very young. Little did I know that I would never stop trying to duplicate it.

In this post, I show you how I duplicated this particular kind of nature. And I did it in my style, as you can see.

To create a drawing of a basalt formation, I actually used a rendered Voronoi diagram, which you see here, transformed it into a subtle perspective, establishing two vanishing points. Then I made three copies arranged as layers in a way that approximated placing them on three-dimensional transparent layers at various depths. This was so I could see the levels, and so the third vanishing point could be right.

Of course, I used Painter's Free Transform to do this!

I kept each layer a little bit transparent so I could get an intuitive feeling for which layer was on the top and which layer was on the bottom. This technique is called depth-cueing.

As you can see, it worked pretty well. I stopped at three layers because I didn't want the drawing project to get too complicated. But, of course, like all of my projects, it soon did!


Next, on a new layer, I drew lines on top of the the lines that I wanted to represent the three-dimensional surface of the basalt formation. This meant choosing a three-dimensional height for each cell. The base layer that extended to the outside of the drawing was the lowest height, of course, and a second and third layer was built on top of it.

This causes cells to raise out of the base layer and appear to become extruded.

When I consulted some real images of basalt formations as a guide, I found that they were quite imperfect and usually were cracked, damaged, or eroded in some way.

I really wanted my drawing to represent a perfect un-eroded result.

I used an extra transparent layer (behind the layer with the lines) and marked each cell with a three-dimensional height index so I could be sure which heights corresponded with each cells. This told me where to put the shading and also told me how to interpret the extrusion lines.

This layer was for informational purposes only. You see here the original small layer with crudely drawn lines. It's actually kind of hard to see the three-dimensional relative positions of the cells in some cases, which is another reason I labelled each cell with a height index.

Once I had designed it, I found that the drawing was way too small to shade the way I like to (using a woodcut technique) and so I resized the image and went over each of the lines by hand to make it crystal clear at the new resolution.

That only took a few days.

Why? After resizing the image, I found that each line was unusually soft. This meant that I had to go over the lines with a small brush, darkening and resolving the line. Then I had to go around it with white to create a clean edge. This is what really took the time!

Naturally I do lots of other things than just draw all the time, and so I had to use extra minutes here and there. I kept the Painter file on my laptop and brought my Wacom tablet with me in my bag.

I spent probably ten or twenty hours drawing this image.

Once the lines were perfect, the next step was shading. But of course it had to be in my style, and this also took quite a bit of time.

I used woodcut shading to create shadows and accessibility shading. This created a very nice look.

To do this, I drew parallel lines at a desired spacing, taking care to make them correspond in length and position to the shading and shadows that would result from a light coming from the left side.

I thickened the lines at their base, and made them a bit triangular. Then at the end, I used a small white brush to erode and sharpen the point and clean the sides of each shading line to get the right appearance.

The final step was coloring the tops and the sides, using a gel layer.

I colored each layer using a different shade of slightly bluish gray. The top layer got the lightest shade.

Here you can see a close-up of the final image, which was very high resolution indeed.

Even though I started out with a computer-generated fracturing pattern, I was able to retain a hand-wrought look to the final image. None of the lines are really computer-prefect

Yes, nature's patterns often take a bit of time to master!