This code uses trigonometric, exponential, and logarithmic functions to define vertex positions, line thicknesses, colors, and point sizes. Through the Manipulate function, users can adjust parameter ‘s’ and see an array of geometric patterns.
In[]:=
DynamicModule[{cols,r,u,verts},cols=RGBColor/@{"#35342f","#f1f2f0"};​​Manipulate[r=1/2-Cos[s]/2+0.2Sin[3s^2]+0.1Cos[4s^3]+0.05Tan[5s^4];​​u=If[s<π,s^2+Sin[s^3]+Cos[Exp[s^2]],s+2πExp[-s^2]+Cos[3s]+Sin[Log[s+1]]];​​verts=Table[(1-r(-1)^(If[s<π,i+1,i])){Cos[2πi/8-u/8-π/8]^3,Sin[2πi/8-u/8-π/8]^3},{i,0,7}];​​Graphics[{Thickness[.005+0.0025Sin[2s^3]+0.001Cos[3s^2]+0.0005Tan[4s]],CapForm["Round"],cols[[1]],Table[Line[{tverts[[i]]+(1-t)RotateRight[verts][[i]],tRotateLeft[verts][[i]]+(1-t)RotateLeft[verts,2][[i]]}],{i,1,7,2},{t,0,1,1/8}],Table[{PointSize[0.01+0.005Cos[4s^2]+0.002Sin[3s^3]+0.001Tan[2s^4]],Blend[{cols[[1]],cols[[2]]},Cos[5s^3]+Sin[4s^2]+Tan[s^3]],Point[Exp[1.2(Cos[s^2]+Sin[s^3])]verts[[i]]]},{i,1,7,2}]},PlotRange->3,ImageSize->540,Background->cols[[2]]],{s,0.,2π}]]
Out[]=
​
s

Acknowledgment

This design was inspired by work from Clayton Shonkwiler 7 years prior.
​https://community.wolfram.com/groups/-/m/t/828023

CITE THIS NOTEBOOK

Parametric curves in art​
by Dashel Myers​
Wolfram Community, STAFF PICKS, April 27, 2024
​https://community.wolfram.com/groups/-/m/t/3165117