Cathedral of Math

Once upon a time, the name of this site was: Theory and Practice of Trying to Combine Just Anything.

Today, I am just trying to combine an experiment in code-generated art – the warp core explosion …

… with my recent attempts to put spherical harmonic functions – “orbitals” – in perspective:

So, I am sketching my warp core function! This could also be seen as an orbital extended to infinity. It looks like a tower with a clover-leaf shaped base. The clover-leaf becomes infinitely large at the base and shrinks to zero in infinite heights.

The shape of the contour lines is described by (cos^2(phi) – sin^2(phi))/z – z being the co-ordinate along the vertical axis and phi the azimuth angle in the xy-plane. But I am just drawing a clover-leaf by putting circles near the corners of a square, to get the curvature about right.

I am starting to explore how to arrange the top view, the side view and the actual perspective projection on the paper. The challenge with perspective drawings is that the interesting projection always looks small compared to the top view. The side view is just a bunch of lines, getting progressively shorter with height – the clover-leaves seen head-on. I eyeball 1/z by freehanding squares and dividing blocks.

I start the construction with pencils – fully freehand but following the rules of perspective drawing as if I would use a ruler. As the drawing progresses, I am coloring the lines with colored pencil – not yet to prettify them but to keep track of what belongs to what.

The clover-leaves are constructed best by locking them up – erecting a mounting frame for them. Not yet quite visible is the biggest challenge: Trying to construct a large clover-leaf whose top view would not fit on the paper. I am creating square tiles on the “floor”, hopping from on the next, using diagonals and intersections.

Finally, the intuitive part starts – adding color with watercolor pencils! I am not yet satisfied. I pick a balanced set of colors before – only to find out, that one color is dominating everything as its shape is so large.

This looks a bit like Easter decoration:

The dark night sky is not flawless as I have already damaged the wet paper, scratching it with a watercolor pencil. The contrast between black and diluted watercolor is harsh.

I pick up my watercolor markers … and I am surprised! I look at the photo, and consider to desaturate the unnaturally vibrant colors. But no – the colors in this photo are faithful!

Now I need to repair the damage of the black spots. Why not test some acrylic pouring? The black turns out nice – like patent leather. I try adding more texture and more bulged “drops” – to make the surface uneven on purpose. The “varnishing” layer also allows me to add white lines on black, as white gel pen lines would turn grey when added directly to the black areas.

All of that works, but I learn something about my gel pens in vibrant blue and pink. (Yes, I always test directly on the artwork – I go all-in!). The ink starts to bleed when I add the resin. It spoils nearly all the white areas. (I cannot bring myself to document this step.)

This is the perfect chance to test my permanent markers. I have nothing to lose! I do not remember how often I have added white over dark and then color again!

Given the adventure and the challenges, I am rather happy with it. But next time I will plan and test a bit more – and perhaps stop messing with the painting before I ruin it!

Now, it needs a name! Semi-consciously, my inspiration has been stained glass. This is: The Cathedral of Math!