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[GIF] Fire in the Hole (Spheres on logarithmic spirals)

Spheres on logarithmic spirals

Fire in the Hole

I'm not exactly sure what to say about this. I was somewhat inspired by Frédéric Vayssouze-Faure's worries bin and I started by plotting Gabriel's Horn. After some playing around, I ended up with the spheres lying on logarithmic spirals on the surface of revolution for the graph of $f(x)=\frac{1}{x^3}$.

This was also the first time I've used Lighting in a nontrivial way, and it was very cool to see how much you can change the mood just by changing the location and color of a couple of point lights.

Here's the code:

With[{δ = π/8., γ = π/5., 
  cols = RGBColor /@ {"#FECEA8", "#E84A5F", "#000000"}},
 Manipulate[
  Graphics3D[{cols[[1]], 
    Table[
     Sphere[{E^((θ - s)/10) Cos[θ + t], 
       E^((θ - s)/10) Sin[θ + t], 
       E^((θ - s)/30)}, .01], {θ, -50. π, 
      4 π, δ}, {t, 0., 2 π, γ}]}, 
   PlotRange -> {{-5, 5}, {-5, 5}, {0, 2}}, ViewAngle -> π/50, 
   ImageSize -> {800, 600}, Boxed -> False, Background -> cols[[-1]], 
   Lighting -> {{"Point", cols[[2]], {0, 0, 1/2}}, {"Directional", 
      cols[[1]], 10 {-1, -1, 1}}}, ViewPoint -> {1, 1, 1}, 
   ViewVertical -> {0, 0, 1}, ViewCenter -> {0.5, 0.5, 0.35}],
  {s, 0, π}]
 ]
POSTED BY: Clayton Shonkwiler
7 Replies
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Sorry, the random ?s were due to a bug in Wolfram Community that wiped out a bunch of special characters; in this case, mostly Greek letters. I've just fixed the above code, so hopefully it will now work.
POSTED BY: Clayton Shonkwiler

That's really cool! Only after removing the View-options I understood the shape of this object, very nice!
POSTED BY: Sander Huisman

Thanks!
POSTED BY: Clayton Shonkwiler

Yep, this marvelous one indeed hypnotized me for a while. Here is the full shape:

With[
{δ =π/8., γ = π/5., s = 0, 
cols = RGBColor /@ {"#FECEA8", "#E84A5F", "#000000"}}, 
Graphics3D[
{cols[[1]], 
Table[Sphere[{E^((θ + s)/10) Cos[θ + t], 
E^((θ + s)/10) Sin[θ + t], 
E^((θ + s)/30)}, .01], {θ, -10. π, 
3 π, δ}, {t, 0., 2 π, γ}]}, 
ImageSize -> {800, 600}, Boxed -> False,
Background -> cols[[-1]],
Lighting -> {{"Point", cols[[2]], {0, 0, 1/2}}, {"Directional", 
cols[[1]], 10 {-1, -1, 1}}},
ViewAngle -> 0.332, 
ViewCenter -> {{0.5`, 0.5`, 0.5`}, {0.602`, 0.359`}},
ViewPoint -> {-0.492`, -1.934`, -0.132`},
ViewVertical -> {0.54`, -0.202`, 4.067`}]
]

enter image description here
POSTED BY: Vitaliy Kaurov

enter image description here - Congratulations! This post is now a Staff Pick! Thank you for your wonderful contributions. Please, keep them coming!
POSTED BY: EDITORIAL BOARD

Hi Clayton,

I am trying to get your fascinating animation to work but am unable to get the code to work in MMA v13.

I am not familiar with the ? construct and cant find any reference to it in the documentation.

Can you point me in the right direction?

Thanks

Jonathan
POSTED BY: Jonathan Kinlay

Thanks Clayton!
POSTED BY: Jonathan Kinlay
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