archery

Notes: 141 6/24/12 — 4:49pm Filed under: #GIF #Mathematica #CTD

Watch in ‘HD’ (1280x720) here

This video shows continuous variation in angle for three different regions of the connect-the-dots algorithm while keeping all other parameters fixed. Unlike the previous video, there is no length contraction of the lines in the iteration. Each instant is a valid 2-coloring.

Music: “Intensives Leben” by Triosk

Mathematica code:

S := 
{{2.8785, .000004, 300, 1000}, 
  {3.05165, .000005, 361, 1070}, 
  {2.6985, .000007 , 301, 929}}

Manipulate[
 ImageCrop[
  Graphics[
   GraphicsComplex[
    Table[
     {-Sin[n*(Part[Part[S, s], 1] + Part[Part[S, s], 2] f)], 
      Cos[n*(Part[Part[S, s], 1] + Part[Part[S, s], 2] f)]}, 
    {n, 0, Part[Part[S, s], 3]}],
   Polygon[Table[i, {i, 1, Part[Part[S, s], 3], 1}]]], 
  PlotRange -> .826787, ImageSize -> 1280],
 {1280, 720}],
{s, {1, 2, 3}}, {f, 1, Part[Part[S, s], 4], 1}]

Notes: 29 6/2/12 — 4:30pm Filed under: #video #2color #CTD #Mathematica #Triosk

This video shows continuous variation in angle (from 0 to Pi) of the connect-the-dots algorithm while keeping all other parameters fixed. Each instant is a valid 2-coloring.

Music: “Derbyshire” by Nerve

Mathematica code:

Manipulate[
  ImageCrop[
   Graphics[
    GraphicsComplex[
     Table[
      {-(.96)^n*Sin[n*.001 f], .96^n*Cos[n*.001 f]}, 
     {n, 0, 300}],
    Polygon[Table[i, {i, 1, 300, 1}]]], 
  PlotRange -> .1, ImageSize -> 640],
 {640, 480}],
{f, 1, 3145, 1}]

Notes: 446 5/27/12 — 6:40pm Filed under: #video #2color #CTD #Mathematica #Nerve

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.9908^n*Sin[n*3.87613], .9908^n*Cos[n*3.87613]}, {n, 0, 750}], Polygon[Table[i, {i, 1, 750, 1}]]], PlotRange -> 1, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.9908^n*Sin[n*3.87613], .9908^n*Cos[n*3.87613]}, {n, 0, 750}],
  Polygon[Table[i, {i, 1, 750, 1}]]], 
 PlotRange -> 1, ImageSize -> 800]

High-res Notes: 11 5/26/12 — 9:59pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.9908^n*Sin[n*3.87613], .9908^n*Cos[n*3.87613]}, {n, 0, 750}], Polygon[Table[i, {i, 1, 750, 1}]]], PlotRange -> .05, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.9908^n*Sin[n*3.87613], .9908^n*Cos[n*3.87613]}, {n, 0, 750}],
  Polygon[Table[i, {i, 1, 750, 1}]]], 
 PlotRange -> .05, ImageSize -> 800]

High-res Notes: 96 5/26/12 — 8:54pm Filed under: #2color #CTD #Mathematica

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.21], .99^n*Cos[n*3.21]}, {n, 0, 700}], Polygon[Table[i, {i, 1, 700, 1}]]], PlotRange -> .4, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.21], .99^n*Cos[n*3.21]}, {n, 0, 700}],
  Polygon[Table[i, {i, 1, 700, 1}]]], 
 PlotRange -> .4, ImageSize -> 800]

High-res Notes: 26 5/26/12 — 7:53pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.99^n*Sin[n*3.21], .99^n*Cos[n*3.21]}, {n, 0, 700}], Polygon[Table[i, {i, 1, 700, 1}]]], PlotRange -> .05, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.99^n*Sin[n*3.21], .99^n*Cos[n*3.21]}, {n, 0, 700}],
  Polygon[Table[i, {i, 1, 700, 1}]]], 
 PlotRange -> .05, ImageSize -> 800]

High-res Notes: 9 5/26/12 — 7:00pm Filed under: #2color #CTD #Mathematica

$800x800 center detail Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.9908^n*Sin[n*3.72802], .9908^n*Cos[n*3.72802]}, {n, 0, 640}], Polygon[Table[i, {i, 1, 640, 1}]]], PlotRange -> 1, ImageSize -> 800]$

800x800

center detail

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.9908^n*Sin[n*3.72802], .9908^n*Cos[n*3.72802]}, {n, 0, 640}],
  Polygon[Table[i, {i, 1, 640, 1}]]], 
 PlotRange -> 1, ImageSize -> 800]

High-res Notes: 7 5/26/12 — 6:00pm Filed under: #2color #CTD #Mathematica

$800x800 Mathematica code: Graphics[ GraphicsComplex[ Table[ {-.9908^n*Sin[n*3.72802], .9908^n*Cos[n*3.72802]}, {n, 0, 640}], Polygon[Table[i, {i, 1, 640, 1}]]], PlotRange -> .25, ImageSize -> 800]$

800x800

Mathematica code:

Graphics[
 GraphicsComplex[
  Table[
   {-.9908^n*Sin[n*3.72802], .9908^n*Cos[n*3.72802]}, {n, 0, 640}],
  Polygon[Table[i, {i, 1, 640, 1}]]], 
 PlotRange -> .25, ImageSize -> 800]

High-res Notes: 13 5/26/12 — 4:53pm Filed under: #2color #CTD #Mathematica

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

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