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Craig S. Kaplan 1. ruj
New blog post: using complex numbers to draw spiral tilings. It's an old idea, but I've always wanted to explain it in full. Plus, this time I include an interactive tool for drawing your own tilings!
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Craig S. Kaplan 1. ruj
Odgovor korisniku/ci @KangarooPhysics
Fantastic! I’d love to know more.
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Daniel Piker 1. ruj
Odgovor korisniku/ci @cs_kaplan
Thanks! It's a conformal mapping formed by superposition of shifted copies of +/- Ln(z) Here's one with an Escher tessellation
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Akiva Weinberger 1. ruj
Odgovor korisniku/ci @KangarooPhysics @cs_kaplan
Imagine a 3D shape of which this is a sequence of slices
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Daniel Piker 2. ruj
Odgovor korisniku/ci @akivaw @cs_kaplan
Funny you should say that! As it happens, I am generating the 3d shape first, and these are the contours
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ricvil 2. ruj
Odgovor korisniku/ci @KangarooPhysics @cs_kaplan
What is math behind this? I would like to understand.
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Daniel Piker 2. ruj
Odgovor korisniku/ci @ricvil3 @cs_kaplan
One way of looking at it is as *potential flow* of an ideal fluid, adding together sources, sinks and vortices as functions of complex numbers. A very nice book that covers this is 'Visual Complex Analysis' by Tristan Needham
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