The Systematic Destruction of a Space-Filling Curve

From August to September 2025, actz commissions curated a collection Line on objkt.com, and I was delighted to add my own piece to the ranks. Each piece was offered as a single edition, 48 hour auction, with a starting bid of 50 tez.

Here it is, although the final piece is unsullied by my brash, egotistic title. It shows my love of fractals and my insistence that entropy will always win. I don't think there's much argument there; it's not a new concept, though I think I'm unlikely to be around to witness the heat death of the universe.

I can, however, manipulate a Hilbert curve and twist it to my wicked way, slowly destroying it in the name of art.

“I felt like destroying something beautiful…”—that man from Fight Club*

The details below give a little more insight into the process of its creation, and show how separate alterations of the algorithm produce sixteen separate examples of a descent into destruction.

Iterations

The piece depicts a Hilbert curve, with a Hausdorff dimension of 2, because in its ultimate form it fills the plane completely. One of the changes, diagonally from the top-left, is the number of iterations.

This image shows the way it works, increasing from left to right.

Noise

The piece also plays with increased Perlin noise, slowly allowing it to swamp the curve and destroy it utterly.

Shearing

To assist with the inevitable destruction of the curve, shearing forces are applied with increasing violence, pulling the thing apart as we move from the top to the bottom of the grid.

Smoothing

Additionally, as we move from left to right, the piece is smoothed with a fairly-simple Chaikin algorithm. Basically, we chop off the corners, with increasing abandon. I suppose, in this case, whilst losing itself, the curve gains more… curves.

Stroke Weight

Stroke weight is also altered, but this is mainly to offset the increased density of the higher iterations, and keep each segment of the grid, no matter how many lines, at the same visual heft.

‘Splatter’

And then a little extra noise, casually termed 'splatters' in the code, for want of a better word. These are like drafting lines, showing the edges and highlighting the turns of the curve. In this example, they're exaggerated slightly, for effect.

*Yes, I do know who, really.