#form constants

Hati og Skoll

clearing a work area

When I was a kid I used to sit off to the side at recess to press on my eyelids so I could see the trippy shapes and patterns and crazy lights that appear... well apparently, these patterns are known as form constants, and have been recorded by ancient cultures all over the world! They also appear when hallucinating, from drugs or a fever or whatever you may have. This article has an explanation of the biology/math/magic side.   

looking deeply into the thing in your hand

img = ImageCrop@DensityPlot[ Sin[2 x - 20 Log[2 (Sin[y]^2 + 1), 2]], {x, 0, 16 Pi}, {y, 0, 32 Pi}, PlotPoints -> 250, ColorFunction -> "SunsetColors", Frame -> False, ImageSize -> 600] LogPolar[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]} d = ImageDimensions[img][[1]] Manipulate[ ImageResize[ ImageTransformation[ ImageTake[ img, {1, 14*d/16}, {1 + (2 - 2 t)*d/32, (32 - 2 t)*d/32}], LogPolar[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], 500], {t, 0, 6/7, 1/7}]

tunnel remember ~ loki mmxii

d[x_, y_, r_, c_, s_, F_, n_] := {Disk[ RotationTransform[n*2.4][{x*c^n, y}], r*c^n], Table[ {White, Disk[ RotationTransform[k*2 Pi/F, RotationTransform[n*2.4][{x*c^n, y}]] [RotationTransform[n*2.4][{x*c^n, y}] + c^n {r - s, 0}], s*c^n]}, {k, 0, F - 1, 1}]} Manipulate[ ImageCrop[ Graphics[ Table[ d[3, 0, 1 - .1*Sin[t + n*Pi/110]^2, 1.025, .03, 24, n], {n, 0, 110, 1}], PlotRange -> 30, Background -> Black, ImageSize -> 700], {500, 700}], {t, 0, 39 Pi/40, Pi/40}] Manipulate[[ ImageCrop[ Graphics[ Table[ d[3, 0, 1 - .1*Sin[t*3 Pi/40 + n*2 Pi/110]^2, 1.025, .03, 24, n], {n, If[t < 66 , 0, 2 (t - 65)], If[t < 56, 2 t, 110], 1}], PlotRange -> 30, Background -> Black, ImageSize -> 700], {500, 700}], {t, 0, 120, 1}]