Mark Megahan
If you happen to have a 3-D printer and you’re looking for something interesting to make with it, consider one of these patterns inspired by common mathematical functions. The latest “mind-bending” category of designs is “math art.” Models which are “essentially visualized versions of mathematical equations, concepts, or theories.” Those without the equipment can still get their hands on these pieces. W&B’s order for a Sierpinski Pyramid will be arriving by mid-December, courtesy of Etsy.
Fractal 3-D printer artwork
If you want to adapt your tabletop 3-D printer for something the whole family can enjoy and learn from, these designs showcased by All3dp magically incorporate “complex geometries and irregular patterns in the design.”
Fractals are especially suited for the new technology. Those are “patterns created by repeating one equation over and over again.”
Besides fractals, there are other amazing and logic defying objects “such as the golden ratio, anti-oloids, and different shapes and structures.” All can be reproduced in variable scale on any 3-D printer.
They begin with unique computer-aided design software programmed to create complex shapes. With the software, “designers can easily make infinite occurrences of an equation to generate a design.” These are only a few of the possibilities.
The experts note that “math art can be very delicate and precise, so most of the time, you should use a small layer height and slow speeds.” That’s crucial to “preserve the model’s structure and detail.”
They suggest that these models should be treated the same as basic “miniatures” because both “contain a lot of detail in a small space.” If you aren’t familiar with the 3-D printer techniques, there are resources available.
A few of the options
As soon as W&B saw the Sierpinski Pyramid, we had to have one. A 10-inch version has already been commissioned and should be waiting under the Christmas tree. Our multicolored desk toy is a fractal pattern of “equilateral triangles that decrease in size and are infinitely self-similar.” The designer claims it’s “half of a Sierpiński octahedron.”
In other words, print two and glue them together into a diamond. One will be just fine for us. If you want to make your own, set your printer so it doesn’t “use supports, bridging, or retraction for this print. As such, it’s suggested to print it in spiral (vase) mode on your slicer and with 0% infill.”
Other popular math inspired objects for use on a 3-D printer are the Hilbert cube, which “uses a mathematical equation to form an endless path.” The distorted torus gives a Möbius twist to the ordinary doughnut.
This pattern uses a “hexagonal pattern all around the piece. After using a hexagonal grid to cover a normal torus, the maker distorted it by pinching and rotating the model to yield the impressive structure and shape you see.”
The pattern called “gyroid” is a standard “infill” pattern for 3-D printer designs. A hunk of it standing alone can make an impressive paperweight or desk fidget toy. Especially with the right paint job. “A gyroid structure is an infinitely connected triply periodic minimal surface, according to the maker.”
Another mind blowing structure is a Klein bottle, where the outside is also the inside. It resembles “a container folding in on itself.” A tricky one is the “so-called Dugaci sculpture.” It “appears to be a knot and looks like it restrains itself with interlocking strands.” You need “tree supports to successfully print this model.” oloid shapes and their inverted anti-oliod are popular too. These versions roll “on its own with a perfect center.“
