Steps towards a pine cone or coronavirus as a function of sines

Tom Veatch

firsty.mp4 Something is better than nothing.
first.mp4 Learning about the variable known as time.
second.mp4 Nice, it's sinusoidal! 0-dimensional.
third.mp4 A sine in 1-d.
fourth.mp4 2-D Sine varying with x and y (and time, shown on z) rectilinearly.
fifth.mp4 2D but varying with radius not x & y. Equal energy in each ring.
sixth.mp4 Semi-3D: 2D wrapped around a sphere. Not equal energy but equal amplitude rings (small rings have less total energy).
seventh.mp4 Equal energy in each ring, again.
eighth.mp4 One going up, another going down, add them together at the same time, you get a standing wave.
ninth.mp4 Two standing waves with different energy levels, different axes on the sphere, different time frequency, different spatial frequency. (There's an absolute value in there to fix: see the discontinuity at one of the equators.
tenthy.mp4 Fixed the absolute value, included some frames from a different run by mistake.
tenthish.mp4 This loop is periodic on the vertical standing wave, but not on the diagonal wave, which jumps 180 degrees at the loop instant.
eleventh.mp4 There we go. Two cycles on the vertical for three cycles on the diagonal. Still equal-energy rings. Pine-cones and coronaviruses aren't so polarly-peaky.
twelfth.mp4 That's getting closer to a pine cone.

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Copyright © 2000-2020, Thomas C. Veatch. All rights reserved.
Modified: July 12, 2020.