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Isometric graph paper!

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Simple isometric Menger sponge with orange striped shading on one face.

Little things make me happy a lot of the time, and fancy graph paper is a pretty little thing — a few bucks for a pad of 50 sheets of the stuff feels like a big pile of promise.

And with the stuff I’ve been doing lately with fractals, grids are a handy thing to have. But a standard square grid doesn’t help as much as I’d like with things like isometric views and triangle-based designs.  You can wing a pseudo-equilateral design on square grid paper by centering a triangle in a 2×2 square, like so:

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Pseudo-equilateral triangles, stretched out to fit a square grid.

But because the length of two of the sides of the triangle are stretched out to make it fit nicely with the gridlines, you don’t get the clean 60 degree angles of a proper equilateral triangle, just a near-ish isosceles approximation.

Which can be fine in a pinch for planning/sketching something triangular or hexagonal, but it’s not very satisfying.

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Three iterations of a Menger sponge, in greyscale marker.

And so: isometric graph paper!  Something for me to use as a guideline for things like Menger sponge layouts, or 60-degree fractal curves like Koch snowflakes. It’s nice to have something that fits an idea exactly instead of requiring a hedge or a compromise.

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Concept sketch for a Menger mug.

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