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Your optimal path across a road, as the level of discomfort from being in the middle of the road increases. In a previous post, the discomfort on the road was constant, but here it smoothly increases towards the centre, resulting in a more realistic smooth S-shaped [or sigmoidal] path. The curve is the same path as would be traced by a ray of light travelling through a material of smoothly varying refractive index. [code] [more]

Your optimal path across a road, as the level of discomfort from being in the middle of the road increases. In a previous post, the discomfort on the road was constant, but here it smoothly increases towards the centre, resulting in a more realistic smooth S-shaped [or sigmoidal] path. The curve is the same path as would be traced by a ray of light travelling through a material of smoothly varying refractive index. [code] [more]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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