archery

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.87], .99^n*Cos[n*3.87]}, {n, 0, 640}], Polygon[Table[i, {i, 1, 640, 1}]]], PlotRange -> 1, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.87], .99^n*Cos[n*3.87]}, {n, 0, 640}],
  Polygon[Table[i, {i, 1, 640, 1}]]], 
 PlotRange -> 1, ImageSize -> 800]

High-res Notes: 6 5/26/12 — 3:56pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.87], .99^n*Cos[n*3.87]}, {n, 0, 640}], Polygon[Table[i, {i, 1, 640, 1}]]], PlotRange -> .25, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.87], .99^n*Cos[n*3.87]}, {n, 0, 640}],
  Polygon[Table[i, {i, 1, 640, 1}]]], 
 PlotRange -> .25, ImageSize -> 800]

High-res Notes: 6 5/26/12 — 2:54pm Filed under: #2color #CTD #Mathematica

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.799], .99^n*Cos[n*3.799]}, {n, 0, 600}], Polygon[Table[i, {i, 1, 600, 1}]]], PlotRange -> 1, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.799], .99^n*Cos[n*3.799]}, {n, 0, 600}],
  Polygon[Table[i, {i, 1, 600, 1}]]], 
 PlotRange -> 1, ImageSize -> 800]

High-res Notes: 2 5/26/12 — 2:00pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.799], .99^n*Cos[n*3.799]}, {n, 0, 600}], Polygon[Table[i, {i, 1, 600, 1}]]], PlotRange -> .25, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.799], .99^n*Cos[n*3.799]}, {n, 0, 600}],
  Polygon[Table[i, {i, 1, 600, 1}]]], 
 PlotRange -> .25, ImageSize -> 800]

High-res Notes: 7 5/26/12 — 1:01pm Filed under: #2color #CTD #Mathematica

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.941], .99^n*Cos[n*3.941]}, {n, 0, 600}], Polygon[Table[i, {i, 1, 600, 1}]]], PlotRange -> 1, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.941], .99^n*Cos[n*3.941]}, {n, 0, 600}],
  Polygon[Table[i, {i, 1, 600, 1}]]], 
 PlotRange -> 1, ImageSize -> 800]

High-res Notes: 3 5/26/12 — 12:45pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.941], .99^n*Cos[n*3.941]}, {n, 0, 600}], Polygon[Table[i, {i, 1, 600, 1}]]], PlotRange -> .25, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.941], .99^n*Cos[n*3.941]}, {n, 0, 600}],
  Polygon[Table[i, {i, 1, 600, 1}]]], 
 PlotRange -> .25, ImageSize -> 800]

High-res Notes: 9 5/26/12 — 12:30pm Filed under: #2color #CTD #Mathematica

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-Sin[n*3.0891], Cos[n*3.0891]}, {n, 0, 300}],
  Polygon[Table[i, {i, 1, 300, 1}]]], 
 PlotRange -> .5391, ImageSize -> 800]

High-res Notes: 122 5/25/12 — 5:52pm Filed under: #2color #CTD #Mathematica

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-Sin[n*2.94712], Cos[n*2.94712]}, {n, 0, 647}],
  Polygon[Table[i, {i, 1, 647, 1}]]], 
 PlotRange -> .5391, ImageSize -> 800]

High-res Notes: 48 5/25/12 — 5:26pm Filed under: #2color #CTD #Mathematica

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-Sin[n*2.66315], Cos[n*2.66315]}, {n, 0, 343}],
  Polygon[Table[i, {i, 1, 343, 1}]]], 
 PlotRange -> .6021, ImageSize -> 800]

High-res Notes: 20 5/25/12 — 5:00pm Filed under: #2color #CTD #Mathematica

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-Sin[n*3.44405], Cos[n*3.44405]}, {n, 0, 218}],
  Polygon[Table[i, {i, 1, 218, 1}]]], 
 PlotRange -> .6021, ImageSize -> 800]

High-res Notes: 21 5/25/12 — 4:30pm Filed under: #2color #Mathematica #CTD

click through for high-res: 500x500

Randomly generated with Mathematica code:

F[r_, a_, s_, p_] :=
 Table[
  Graphics[
   GraphicsComplex[
    Table[
     {-(r^n)*Sin[n*a], r^n*Cos[n*a]}, {n, 0, s}],
    {If[G == 1, White, Black], Polygon[Table[i, {i, 1, s, 1}]]}], 
   PlotRange -> p, ImageSize -> 500, 
   Background -> If[G == 0, White, Black]],
  {G, {0, 1}}]

Manipulate[
  F[r, a, s, p],
{{p, 1}, .0001, 1, .001}, {{r, 1}, .95, 1}, {{a, 2.8}, 0.001, 4Pi, .00001}, {{s, 300}, 1, 1000, 1}]

 ListAnimate[F[r, a, s, p], 20, AnimationRunning->False]

Notes: 44 5/17/12 — 9:07pm Filed under: #2color #2frame #CTD #GIF #Mathematica #epilepsy warning

Consider a 2-coloring of some region and its complement:

They are the same except that the black and white colors have been interchanged. Recall that these are the only possible 2-colorings for this partition.

By construction, for any planar 2-coloring, if the two images are displayed at the same time by overlaying the two images and treating white as a transparent color, then a region in all black results

… nothing too interesting.

Instead, displaying the two images in rapid succession creates a dynamic strobe effect.

Its like you can start with nothing, divide it into things which are still and inert when taken individually, yet end up with something dynamic and alive when taken together.

Mathematica code:

F[ a_, s_, p_] :=
 Table[
  Graphics[
   GraphicsComplex[
    Table[
     {-Sin[n*a], Cos[n*a]}, {n, 0, s}],
    {If[G == 1, White, Black], Polygon[Table[i, {i, 1, s, 1}]]}], 
   PlotRange -> p, ImageSize -> 500, 
   Background -> If[G == 0, White, Black]],
  {G, {0, 1}}]

Manipulate[
  F[ a, s, p],
{{p, 1}, .0001, 1, .001}, {{a, 2.8}, 0.001, 4Pi, .00001}, {{s, 300}, 1, 1000, 1}]

 ListAnimate[F[a, s, p], 20, AnimationRunning->False]

Notes: 43 5/16/12 — 6:31pm Filed under: #GIF #2color #2frame #CTD #Mathematica #epilepsy warning #wisdom

view GIFs in hi-res here (700x700)

Mathematica code:

F[a_, L_, r_, s_, t_] :=
 Table[
  {-(r + s*Cos[t])^n*Sin[n*a], (r + s*Cos[t])^n*Cos[n*a]}, {n, 0, L}]

V := 
 {{1.45631, 556, .995, .003}, {2.94712, 502, .998, .001}, 
 {4.50891, 485, .9955, .0025}, {4.9367, 630, .997, .002}}

Table[
 ListAnimate[
  Table[
   Graphics[
    Polygon[
     F[Part[Part[V, G], 1], Part[Part[V, G], 2], Part[Part[V, G], 3], Part[Part[V, G], 4], t]], 
   PlotRange -> 1, ImageSize -> 250],
 {t, 0, 2 Pi, 2 Pi/40}]],
{G,1,4,1}

Notes: 273 5/10/12 — 6:18pm Filed under: #2color #CTD #GIF #Mathematica #photoset

hi-res GIFs (700x700)

Mathematica code:

F[a_, L_, r_, s_, t_] :=
 Table[
  {-(r + s*Cos[t])^n*Sin[n*a], (r + s*Cos[t])^n*Cos[n*a]}, {n, 0, L}]

V := 
 {{1.45631, 556, .995, .003}, {2.94712, 502, .998, .001}, 
 {4.50891, 485, .9955, .0025}, {4.9367, 630, .997, .002}}

Table[
ListAnimate[
 Table[
  Graphics[
   Polygon[
    F[Part[Part[V, G], 1], Part[Part[V, G], 2], Part[Part[V, G], 3], Part[Part[V, G], 4], t]], 
   PlotRange -> 1, ImageSize -> 700],
  {t, 0, 2 Pi, 2 Pi/40}]], 
{G,1,4,1}

Notes: 21 5/10/12 — 6:02pm Filed under: #GIF #Mathematica #2color #CTD

$Mathematica code: ListAnimate[ Table[Show[ Table[Graphics[ GraphicsComplex[ Table[ {-(.975 + .025*Mod[.5 t + .5 G, 1])^n*Sin[n*3.586], (.975 + .025*Mod[.5 t + .5 G, 1])^n*Cos[n*3.586]}, {n, 0, 416}], {Opacity[(G +(.3+ t) (-1)^G)], Polygon[Table[i, {i, 1, 416, 1}]]}], PlotRange -> .04, ImageSize -> 500], {G, {0, 1}}]],{t, 0, .95, .05}]]$

Mathematica code:

ListAnimate[
 Table[Show[
   Table[Graphics[
     GraphicsComplex[
      Table[
       {-(.975 + .025*Mod[.5 t + .5 G, 1])^n*Sin[n*3.586],
          (.975 + .025*Mod[.5 t + .5 G, 1])^n*Cos[n*3.586]},
      {n, 0, 416}],
    {Opacity[(G +(.3+ t) (-1)^G)], Polygon[Table[i, {i, 1, 416, 1}]]}], 
    PlotRange -> .04, ImageSize -> 500],
  {G, {0, 1}}]],
{t, 0, .95, .05}]]

Notes: 613 5/9/12 — 5:00pm Filed under: #GIF #Mathematica #2color #CTD