In last weeks post, we saw how the motion of particles that move along straight lines creates the illusion of a spinning circle. This time we actually let the individual particles move in circular paths and observe various patterns that result when the relative phase of each particle is varied. Here, “phase” just means where along the circular path a certain particle is when compared to the others.

In the first animation, each of the particles arrive at the edge of the black circle at the same time to create the effect of a spinning and contracting/expanding circle.

In the second animation, the particles are phased just right to create the illusion of a circle that slides along the edge of the black circle. This is similar to the Tusi motion from the previous post except in this instance the circle doesn’t spin.

In the third animation, the phases are adjusted to make it seem like the particles move along a straight line that spins around, but really each particle is still only moving along a circular path. This is a somewhat opposite effect from the Tusi motion where the particles were always moving along straight lines.

Inspired by the not-Tusi-couple.

Mathematica code:

Manipulate[

Graphics[

{{Black,

Disk[{0, 0}, 1.05]},

Table[

Rotate[

{White, Opacity[o],

Circle[{.525, 0}, .525]},

n*2 Pi/m, {0, 0}],

{n, 1, m, 1}],

Table[

Rotate[

{White,

Disk[

.525 {1 + Cos[-2 Pi (p*n/m + t)], Sin[-2 Pi (p*n/m + t)]}, .02]},

n*2 Pi/m, {0, 0}],

{n, 1, m, 1}]},

PlotRange -> 1.1, ImageSize -> 500],

{{m, 8, "circles"}, 1, 20, 1},

{{o, .5, "path opacity"}, 1, 0},

{{p, 0, "phase"}, 0, 2, 1},

{t, 0, 1}]