The Fractal Pyramid: A Model to Appreciate

Disclaimer: this fractal pyramid model is not mine nor of my creation. It was made by ricktu and published under the Creative Commons - Attribution license (link:


The fractal pyramid - a marvel of math. It has a finite volume, so you can fill it with water, but an infinite surface area, so all the paint in the world would not be able to cover it.

Here's my little rant about why it's going to make you love your 3D printer.


The first layer is already enough to drop your draw. I printed this out with 4 iterations (4 repeats of self-similarity within the pyramid) and 4 cm base lengths, which is already pretty darn small - but the first thing the printer does is lay down 256 squares, each 2.5 mm wide. It's insane. You watch a tiny grid appear from out of the nozzle, quite literally materializing onto the print bed. Absolutely mesmerizing.

Then the print head goes through and fills in all 256 squares with dots of plastic just slightly larger than the nozzle orifice (0.4mm), all in less than a minute. That in itself is already enough to make you appreciate that you have a machine to do the work.

My fingers for reference.


But the true jaw-dropper, even for someone who's been into 3D printing as long as I have, is when the patterns come in. The nozzle lays down microscopic lines of plastic with a speed and precision that evolution itself should be jealous of -- most of the time, you literally can't see the print head moving: you only can hear the vibrations. The motion belts and pulleys barely even twitch in one direction before snapping around to twitch in the other direction, a true tribute the stepper motors' microstepping abilities.

All the while, don't forget that fractal pyramids have a continuous cross-section, so after laying down the initial layers, the print head can just spiral up the model in vase mode (spiralize the outer contour in Cura). Sure, there's a blob of plastic at the peak of the pyramid, but you can't blame some plastic for leaking out when the printhead paused at the end of the print. I mean, that peak is tiny.


I think it's rather difficult to describe the sensation of watching a fractal pyramid form, but I hope I got the point across: for those of you who've been printing nothing but functional designs for a long while, this is going to make you appreciate your printer again. It's something you have to see to believe.



Leave a Reply

Your email address will not be published. Required fields are marked *