Euler walks

This is the first 10000 digits of e (the base of the natural logarithm), as interpreted by a spiral walk determined by each successive digit:

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And here is a similar interpretation for γ (the Euler-Mascheroni constant):

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Pi walk

This is the first 10000 digits of π, as interpreted by a spiral walk, with each step of the walk determined by each digit. In other words, if the first digits are “3.1415…” then we walk up 3 pixels, then left 1 pixel, then down 4 pixels, then right 1 pixel, then up 5 pixels, and so on, while painting each step of the walk with a different random color.

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Ulam’s spiral in your browser

My day-to-day work is focused mostly on Android and Windows development, so I often find myself a bit disconnected from web development. I thought I’d go through a few random exercises in JavaScript, and simultaneously bring some of my oldie-but-goodie projects “up to date,” as it were. A long time ago I made a Windows application that displays the Ulam prime number spiral, but there’s no reason it can’t be done in the browser today, so here we go:

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Highlight twin primes
Highlight Mersenne primes

The above picture is dynamically generated in your browser. Go ahead and interact with it: you can use your mouse scroll wheel to zoom in and out, and use the checkboxes to highlight certain special types of primes.