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If you were to start on the equator, pick a compass bearing between North and East, and then keep moving in exactly that bearing, what path would you take? You would spiral in towards the North pole, winding tighter and tighter, following a course called a loxodrome. On many maps of the world, this would look like a straight line. This animation shows a loxodrome spiral on a rotating globe. The shadow it casts from a light source at the top of the globe creates a logarithmic spiral which is inverted on itself as the globe spins. The logarithmic spiral is a self-similar curve which often appears in nature. [more] [code]

If you were to start on the equator, pick a compass bearing between North and East, and then keep moving in exactly that bearing, what path would you take? You would spiral in towards the North pole, winding tighter and tighter, following a course called a loxodrome. On many maps of the world, this would look like a straight line. This animation shows a loxodrome spiral on a rotating globe. The shadow it casts from a light source at the top of the globe creates a logarithmic spiral which is inverted on itself as the globe spins. The logarithmic spiral is a self-similar curve which often appears in nature. [more] [code]

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    Does that make a loxodrome the preimage of a logarithmic spiral through a mobius transformation?
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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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