Sines in Many Directions

summary:

When the input never moves in space, the output of oscillating points is easier to understand.

description:

Each of these sets of events starts out pointing in a different direction. Yet the x, y, and z values of the input is never altered. This is why you can spot the spatial origin, the point in the center of all the moving points. It would be simple enough to shift these arbitrary oscillators around precisely the origin to arbitrary oscillators around arbitrary points - just add in an arbitrary value as a last step.

command:
q_graph -loop 0 -box 12 -dir vp -out sines_xyz_constant -command 'q_add_n -50 2 2 1 .05 0 0 0 2000 | q_sin' -color red -command 'q_add_n -50 -2.5 0 .5 .05 0 0 0 2000 | q_sin' -color blue -command 'q_add_n -50 0 1.9 -2.3 .05 0 0 0 2000 | q_sin' -color green -command 'q_add_n -50 2 .8 2.2 .05 0 0 0 2000 | q_sin' -color orange -command 'q_add_n -50 1.5 -1 -1.8 .05 0 0 0 2000 | q_sin' -color black -command 'q_add_n -50 -1.5 -2.4 0 .05 0 0 0 2000 | q_sin' -color aqua -command 'q_add_n -50 -1.8 1.5 1.6 .05 0 0 0 2000 | q_sin' -color purple
math
equation:

$\sin(t,\vec{R}) = (\sin(t) \cosh(|R|), \cos(t) \sinh(|R|) \frac{\vec{R}}{|R|})$

tags
Physics Tag:
simple harmonic oscillator
Math Tag:
trig functions
sine
Programming Tag:
command line quaternions