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If we have a bunch of points that are uniformly spaced, we can squeeze them radially so that they yield a halftoned image. For example, if we have points distributed along a phyllotactic spiral, we can squeeze them to get a skull: How does this work? Math math math. As usual, we want to match […]

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## Approximate TSP Paths

Let’s say you have lots of points, and you want to visit them rapidly. And you’re too lazy to solve the full TSP. How well do different approximations work? That is, how far would you have to travel to visit each point? Let’s say you have N points that are uniformly randomly distributed in a […]

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## Scribble Art

Let’s scribble! There are other papers that have used scribbling for halftoning images, but I want to add a bit more math. A simple model is to have a circle that travels along a base curve. We can parameterize this as: . To use this for halftoning, we should know the curve length (per period) […]

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## HalftonePAL

HalftonePAL is a program written in Processing that lets you make halftoned versions of your images using circles, dots, and lines. You can change the size of the shapes, which pattern to use, switch between black or white paper (and the opposite ink), and more! It can save the output as SVG, JPG, or TXT […]

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## Approximate Circle Packing

I’d like to be able to have a region that is densely packed with non-overlapping circles, whose sizes vary spatially in a pre-defined way. There are lots of resources for Poisson-disk sampling, but that doesn’t result in snugly packed circles. Time to do some tinkering! Random search The laziest way to do this: try to […]

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## Renaming Cities Based on their Coordinates

While driving through Normandy, I was struck by the wackiness of a lot of the local place names. This is amplified by the large linguistic flow through the area, and local dialects that I’m not familiar with, but still felt very silly. For example: Looking at names like these, I figured that I could make […]

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## New Image via Cut-and-Paste

Previously, (1, 2) I’ve chopped one picture into square sections to make a new image. This time, I want to take freeform sections from a larger image to make a smaller one. This is basically like taking scissors to a magazine, then putting together the pieces to make a new picture. Let’s call the magazine […]

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## Lithophane-based Hidden Images

I received a comment with a great idea: try to hide images in pairs of lithophanes! Lithophanes are thin sheets of an opaque and translucent material with varying thickness that display an image when held up to light. The image is bright where the material is thin, and dark where the material is thick. Previously, […]

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## Four Images from Two Transparencies

Previously, I used polarized sheets to generate images. That’s too complicated to physically make, so it’s time to try something else. How about just two transparent films with black marks? Then we can try to encode four images that are revealed by overlapping the two, and rotating the top film. This sort of rotation problem […]

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## Polarization Images

Have you ever played with polarized films? If they’re aligned, they look transparent. If they-re misaligned by 90 degrees, they become opaque. Let’s use this to make pictures! The intensity of transmission is governed by Malus’s Law, which says that the intensity is , where is the misalignment of the two films. Now how can […]