Wolfram Cloud Document

The animation is made of mostly 𝒔𝒊𝒏(𝒙), 𝒄𝒐𝒔(𝒙). It’s interesting to note that periodicity is key to time measurement. For example:

1 whale’s heart beat ~ 500 flaps of hummingbird.

Here it is easy to observe relations of 3 rhythms:

Full 1 circle of the jellyfish is:

3 cycles of the sea-worm wiggle

16 cycles of the jellyfish flap

Time is relative not only in Einstein’s theories, but also in how living beings experience it. Any clock is a process and any rhythm is a clock. We measure duration of one process by the beat of another. A clock would slow down near a black hole, but also heart beat clock can slow down during sleep or diving or speed up when danger is around. Time drags when we are bored and flies when we play. While physics equations can look at a time as space, we can return to the same location but never to the same moment. While in Block Universe all moments of time exist, mind exists only in a single moment that keeps changing. It feels like our consciousness is dragged through the time dimension of the Block Universe. Time is rich and has many mysteries.

Example of a set of 𝐟𝐨𝐫𝐦𝐮𝐥𝐚𝐬 describing a 𝐬𝐢𝐧𝐠𝐥𝐞 𝐜𝐫𝐞𝐚𝐭𝐮𝐫𝐞 mathematically. Quite elegant and compact, considering how complex the visual looks. The variables {𝒙,𝒚} run a uniform range of points generating creature points {𝑿, 𝒀} through these formulas transformations.

There is a talented artist on 𝕏 doing sophisticated designs with simple but elegant P5.JS Processing code. Designs usually are reminiscent of some fantastical sea creatures or other live organisms. The code from here:

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https://x.com/yuruyurau/status/1933629116575855091

a=(x,y,d=mag(k=(4+sin(y*2-t)*3)*cos(x/29),e=y/8-13))=>point((q=3*sin(k*2)+.3/k+sin(y/25)*k*(9+4*sin(e*9-d*3+t*2)))+30*cos(c=d-t)+200,q*sin(c)+d*39-220)
t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/240,i=1e4;i--;)a(i,i/235)}

◼

https://x.com/yuruyurau/status/1927373647125119025

a=(x,y,d=mag(k=9*cos(x/8),e=y/8-12.5)**2/99+sin(t)/6+.5)=>point((q=99-e*sin(atan2(k,e)*7)/d+k*(3+cos(d*d-t)*2))*sin(c=d/2+e/69-t/16)+200,(q+19*d)*cos(c)+200)
t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,66);for(t+=PI/45,i=1e4;i--;)a(i%200,i/55)}

was translated in the Wolfram Language

a1[x_, y_, t_] := Module[ {k, e, d, c, q}, k = (4 + 3*Sin[2*y - t]) * Cos[x/29]; k = If[Abs[k] < 10^-10, 10^-10, k]; e = y/8 - 13; d = Norm[{k, e}]; c = d - t; q = 3*Sin[2*k] + 0.3/k + Sin[y/25]*k*(9 + 4*Sin[9*e - 3*d + 2*t]); {q + 30*Cos[c] + 200, q*Sin[c] + 39*d - 220}]

a2[x_, y_, t_] := Module[ {k, e, d, c, q, t2 = (16/3)*t}, k = 9*Cos[x/8]; e = y/8 - 12.5; d = (k^2 + e^2)/99 + Sin[t2]/6 + 0.5; c = d/2 + e/69 - t2/16; q = 99 - e*Sin[7*ArcTan[k, e]]/d + k*(3 + 2*Cos[d*d - t2]); {q*Sin[c] + 200, (q + 19*d)*Cos[c] + 200}]

And can be animated with Manipulate in a notebook:

Manipulate[ points1 = Table[a1[i, i/235, t], {i, 0, 9999}]; points2 = Table[a2[Mod[i, 200], i/55, t], {i, 0, 9999}]; Graphics[ { {RGBColor[0.99, 0.7, 0.7, 0.99], PointSize[.0015], Point[points1]}, {RGBColor[0.7, 0.99, 0.9, 0.7], PointSize[.001], Point[points2]} }, Background -> RGBColor[0.035, 0.035, 0.035], PlotRange -> {{0, 400}, {0, 400}}, ImageSize -> 550 ], {t, 0, 6 Pi, Pi/240}]

Or animated as stand alone .MP4 video via AnimationVideo:

In[]:=

Parallelize@AnimationVideo[ points1 = Table[a1[i, i/235, t], {i, 0, 9999}]; points2 = Table[a2[Mod[i, 200], i/55, t], {i, 0, 9999}]; Graphics[ { {RGBColor[0.99, 0.7, 0.7, 0.99], PointSize[.0015], Point[points1]}, {RGBColor[0.7, 0.99, 0.9, 0.7], PointSize[.001], Point[points2]} }, Background -> RGBColor[0.035, 0.035, 0.035], PlotRange -> {{0, 400}, {0, 400}}, ImageSize -> 550 ], {t, 0, 6 Pi, Pi/240}, RasterSize->720{1,1},DefaultDuration->25]

Out[]=

CITE THIS NOTEBOOK

Deep sea satellite: translating from P5.JS processing to Wolfram
by Vitaliy Kaurov
Wolfram Community, STAFF PICKS, June 17, 2025
https://community.wolfram.com/groups/-/m/t/3480601