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RSS Feed for Wolfram Community showing any discussions in tag Visual Arts sorted by activeHypocycloid Art #5
http://community.wolfram.com/groups/-/m/t/1267384
"THEY LIE ON ONE SINGLE HIDDEN [CIRCLE]."
![Hypo art][1]
Mixing of a visual language with one of calculus, specifically hypocycloids. to create dynamic compositions that merge two aspects of design that seem to rarely meet - the idea of the two seemingly conflicting studies, art and math, combined into something that both parties understand and can appreciate.
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=hypo-08.jpg&userId=1267133Jes Rose2018-01-18T03:41:28ZHypocycloid Art #4
http://community.wolfram.com/groups/-/m/t/1267375
![Hypocycloid Art][1]
"THE CONFIGURATION OF KISSING CIRCLES CLOSE UP."
Mixing of a visual language with one of calculus, specifically hypocycloids. to create dynamic compositions that merge two aspects of design that seem to rarely meet - the idea of the two seemingly conflicting studies, art and math, combined into something that both parties understand and can appreciate.
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=hypo-07.jpg&userId=1267133Jes Rose2018-01-18T03:38:22ZHypocycloid Art #3
http://community.wolfram.com/groups/-/m/t/1267365
![hypo art][1]"
THESE CURVES POSSESS MANY REMARKABLE PROPERTIES."
Mixing of a visual language with one of calculus, specifically hypocycloids. to create dynamic compositions that merge two aspects of design that seem to rarely meet - the idea of the two seemingly conflicting studies, art and math, combined into something that both parties understand and can appreciate.
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=hypo3-02.jpg&userId=1267133Jes Rose2018-01-18T03:17:53ZRolling Hypocycloid Art #2
http://community.wolfram.com/groups/-/m/t/1267355
"![hypocycloid design][1]
"NOT CONVINCED JUST BY LOOKING AT THESE PICTURES?"
Mixing of a visual language with one of calculus, specifically hypocycloids, to create dynamic compositions that merge two aspects of design that seem to rarely meet - the idea of the two seemingly conflicting studies, art and math, combined into something that both parties understand and can appreciate.Jes Rose2018-01-18T03:11:59ZRolling Hypocycloid Art
http://community.wolfram.com/groups/-/m/t/1267346
"![hypocycloid design][1]
IT IS NOT ALWAYS THE CASE THAT ONE CAN FIND A SERIES OF CIRCLES KISSING EACH OTHER SO PRECISELY AS THUS."
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=hypocycloid-01.jpg&userId=1267133
Mixing of a visual language with one of calculus, specifically hypocycloids. to create dynamic compositions that merge two aspects of design that seem to rarely meet - the idea of the two seemingly conflicting studies, art and math, combined into something that both parties understand and can appreciate.Jes Rose2018-01-18T03:10:47Z[GIF] All Day (Hamiltonian cycle on the 24-cell)
http://community.wolfram.com/groups/-/m/t/1265322
![Stereographic projection of a Hamiltonian cycle on the 24-cell][1]
**All Day**
Same idea as [_Touch ’Em All_][2]: this is the stereographic image of a Hamiltonian cycle on the 24-cell. The idea behind the code is the same, so look back at that post for an explanation (as before, the definition of `ProjectedSphere[]` is not reproduced here; see [_Inside_][3]).
Stereo[{x1_, y1_, x2_, y2_}] := {x1/(1 - y2), y1/(1 - y2), x2/(1 - y2)}
smootherstep[t_] := 6 t^5 - 15 t^4 + 10 t^3;
twenty4cellvertices = Normalize /@
DeleteDuplicates[
Flatten[
Permutations /@ ({-1, -1, 0, 0}^Join[#, {1, 1}] & /@ Tuples[{0, 1}, 2]), 1]
];
sorted24CellVertices =
Module[{v = twenty4cellvertices, M, Γ, cycle},
M = Table[
If[v[[i]] != -v[[j]] && HammingDistance[v[[i]], v[[j]]] == 2, 1,
0], {i, 1, Length[v]}, {j, 1, Length[v]}];
Γ = AdjacencyGraph[M];
cycle = FindHamiltonianCycle[Γ];
v[[#[[1]] & /@ (cycle[[1]] /. UndirectedEdge -> List)]]
];
DynamicModule[{θ, viewpoint = 1/2 {-1, 1, 1},
pts = N[sorted24CellVertices],
cols = RGBColor /@ {"#04E762", "#00A1E4", "#DC0073", "#011627"}},
Manipulate[
θ = π/3 smootherstep[t];
Graphics3D[{Specularity[.4, 10],
Table[
ProjectedSphere[RotationMatrix[θ, {pts[[i]], pts[[Mod[i + 1, Length[pts], 1]]]}].pts[[i]], .2],
{i, 1, Length[pts]}]},
PlotRange -> 4.5, ViewAngle -> π/3, ViewPoint -> viewpoint,
Boxed -> False, Background -> cols[[-1]], ImageSize -> 540,
Lighting -> {{"Directional", cols[[1]],
50 {1, -1, 2}}, {"Directional", cols[[2]],
50 {1, 2, -1}}, {"Directional", cols[[3]],
50 {-2, -1, -1}}, {"Ambient", cols[[-1]]}}],
{t, 0, 1}]
]
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=proj14q.gif&userId=610054
[2]: http://community.wolfram.com/groups/-/m/t/1263478
[3]: http://community.wolfram.com/groups/-/m/t/1260753Clayton Shonkwiler2018-01-13T19:57:21Z[GIF] Fall Out (Rotating circle on the projective plane)
http://community.wolfram.com/groups/-/m/t/1239487
![Rotating circle on the projective plane][1]
_Fall Out_
This was a result of various experiments mapping from the sphere to the plane.
In this case, I'm taking a circle of disks on the sphere, then mapping to the plane by the following map: each point on the sphere (except those on the equator) is sent to the point on the $z=1$ plane lying on the same line through the origin (this map arises as a way of identifying [most of] the projective plane with an actual plane). Then, apply the inversion in the unit circle $z \mapsto \frac{z}{|z|^2}$.
The circle on the sphere is the orbit of the point $p = (0,1/2,\sqrt{3}/2)$ under rotations around $(\cos s, 0 \sin s)$. Here $s$ is treated as the time parameter and varies from $0$ to $\pi$.
Here's the code:
inversion[p_] := p/Norm[p]^2;
With[{n = 141, d = .01, p = {0, 1/2, Sqrt[3]/2},
b = NullSpace[{N[{0, 1/2, Sqrt[3]/2}]}],
cols = {Black, GrayLevel[.95]}},
Manipulate[
Graphics[
{PointSize[.01], cols[[1]],
Polygon /@
Table[inversion[#1[[1 ;; 2]]/#1[[3]]]
&[RotationMatrix[t, {Cos[s], 0, Sin[s]}].(Cos[d] p + Sin[d] (Cos[θ] b[[1]] + Sin[θ] b[[2]]))],
{t, 0., 2 π, 2 π/n}, {θ, 0., 2 π - 2 π/20, 2 π/20}]},
PlotRange -> 4, ImageSize -> 540, Background -> cols[[-1]]],
{s, 0., π}]]
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=dots4.gif&userId=610054Clayton Shonkwiler2017-12-05T05:25:23Z[GIF] Microcosm (Stereographic projection of cube grid)
http://community.wolfram.com/groups/-/m/t/1225032
![Stereographic projection of cube grid][1]
**Microcosm**
This is conceptually very simple: take a $7 \times 7$ grid of unit cubes in space, normalize to the unit sphere, stereographically project to the plane, then apply a rotation to the original grid of cubes. Here's the code:
Stereo[p_] := 1/(1 - p[[-1]]) p[[;; 2]];
With[{n = 3, cols = RGBColor /@ {"#4EEAF6", "#291F71"}},
Manipulate[
Graphics[
{Opacity[.5], CapForm[None], cols[[1]], Thickness[.006],
Line[
Flatten[
Transpose[
Table[
Stereo[Normalize[#]] & /@
{{t,
y Cos[θ] - z Sin[θ],
z Cos[θ] + y Sin[θ]},
{y, t Cos[θ] - z Sin[θ],
z Cos[θ] + t Sin[θ]},
{y, z Cos[θ] - t Sin[θ],
t Cos[θ] + z Sin[θ]}},
{z, -n - 1/2, n + 1/2}, {y, -n - 1/2, n + 1/2}, {t, -n - 1/2.,
n + 1/2, 1/20}],
{2, 3, 4, 1, 5}],
2]
]
},
PlotRange -> 1, Axes -> False, ImageSize -> 540, Background -> cols[[-1]]],
{θ, 0, π/2}]
]
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=rotateStereo12c.gif&userId=610054Clayton Shonkwiler2017-11-20T05:51:30Z[GiF] Hip to be square
http://community.wolfram.com/groups/-/m/t/1256276
After being a life long Macbook Pro user, I just switched and bought a Surfacebook 2. Here's an homage to the squareness of Windows:
![enter image description here][1]
w=1920;h=1080;d=60;t=1;
f[t_] := Module[{fillStyle,q,e,o},
Reap[For[q=0,q<w,q+=d*2,
For[e=0,e<h,e+=d*2,
fillStyle=RGBColor[Sin[t+e],Cos[2-e],Cos[t+q+e],Cos[t+q+e]];
o=(d*Cos[t+q]);
Sow@{fillStyle,Rectangle[{q+o,e-o},{q+o,e-o}+{d+o,d+o}]}
]
]][[2,1]]
];
Graphics[Dynamic[f[t++0.05]], PlotRange->{{0,w},{0,h-80}}*(t), ImageSize->500, Background->Black]
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=windows.gif&userId=900170Mike Sollami2018-01-01T08:24:06Z