archery

Posts tagged: density plot

$Made in response to a recent question posted at the Mathematica Stack Exchange. Mathematica code: img = ImageCrop@DensityPlot[ Sin[2 x - 20 Log[2 (Sin[y]^2 + 1), 2]], {x, 0, 16 Pi}, {y, 0, 32 Pi}, PlotPoints -> 250, ColorFunction -> "SunsetColors", Frame -> False, ImageSize -> 600]LogPolar[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}d = ImageDimensions[img][[1]] Manipulate[ ImageResize[ ImageTransformation[ ImageTake[ img, {1, 14*d/16}, {1 + (2 - 2 t)*d/32, (32 - 2 t)*d/32}], LogPolar[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], 500], {t, 0, 6/7, 1/7}]$

Made in response to a recent question posted at the Mathematica Stack Exchange.

Mathematica code:

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}]

Notes: 616 5/5/13 — 6:00pm Filed under: #logpolar coordinates #form constants #density plot #GIF #Mathematica

$Mathematica code: Animate[ DensityPlot[ Cos[Exp[Sqrt[x^2 + y^2]]*Sin[ArcTan[x, y]] + t], {x, -7, 7}, {y, -7, 7}, PlotPoints -> 150, Mesh -> False, Frame -> False, ColorFunction -> GrayLevel, ImageSize -> 521],{t, 0, 2 Pi, 2 Pi/10}]$

Mathematica code:

Animate[
  DensityPlot[
    Cos[Exp[Sqrt[x^2 + y^2]]*Sin[ArcTan[x, y]] + t], 
    {x, -7, 7}, {y, -7, 7},
  PlotPoints -> 150, Mesh -> False, Frame -> False, 
  ColorFunction -> GrayLevel, ImageSize -> 521],
{t, 0, 2 Pi, 2 Pi/10}]

Notes: 115 7/1/12 — 5:00pm Filed under: #GIF #Mathematica #density plot #drafts #queued

Music: “Parisian Goldfish (Take Remix)” by Flying Lotus

Watch the rest of the video in sub-par quality here.
When it comes to the rapid movement of unnaturally bright colors Tumblr’s video transcoding seems to work better than both Vimeo’s and YouTube’s!

Mathematica code:

ListAnimate[
 Table[
  ImageCrop[
   DensityPlot[
    Sin[(t*.005)*Abs[(x + I y)^2]], {x, -8, 8}, {y, -8, 8}, 
   PlotPoints -> 20, Mesh -> False, Frame -> False, 
   ColorFunction -> Hue, ImageSize -> 668],
   {640, 480}],
 {t, 0, 1780, 1}]
20, AnimationRunning -> False]

Notes: 8 3/28/12 — 5:01pm Filed under: #Mathematica #video #Flying Lotus #density plot

Mathematica code:

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
     ImageResize[ImageTake[ImageCrop[
       DensityPlot[
         Sin[104.02*Abs[(x + I y)^2]], 
       {x, -4.26, 4.26}, {y, -4.26, 4.26}, PlotPoints -> 27, 
       Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834],
     800], {193 - t, 747 - t}, {123 + t, 677 + t}], {500, 500}],
    f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
 {t, 63, 0, 7}],
10, AnimationRunning -> False]

Notes: 58 3/27/12 — 6:08pm Filed under: #GIF #Mathematica #logpolar coordinates #density plot

$High-res: 800x800 Mathematica code: f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}ImageTransformation[ ImageCrop[ DensityPlot[ Sin[104.02*Abs[(x + I y)^2]], {x, -4.26, 4.26}, {y, -4.26, 4.26}, PlotPoints -> 27, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800],f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]$

High-res: 800x800

Mathematica code:

f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}

ImageTransformation[
 ImageCrop[
    DensityPlot[
       Sin[104.02*Abs[(x + I y)^2]], 
    {x, -4.26, 4.26}, {y, -4.26, 4.26}, 
    PlotPoints -> 27, Mesh -> False, Frame -> False, 
    ColorFunction -> Hue, ImageSize -> 834],
 800],
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]

High-res Notes: 16 3/27/12 — 5:00pm Filed under: #Mathematica #logpolar coordinates #density plot

$Mathematica code: f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}ListAnimate[ Table[ ImageTransformation[ ImageResize[ImageTake[ImageCrop[ DensityPlot[ Sin[104.54*Abs[(x + I y)^2]], {x, -2.5, 2.5}, {y, -2.5, 2.5}, PlotPoints -> 27, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800], {100 + t, 700 + t}, {100 - t, 700 - t}],{500, 500}], f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], {t, 0, 90, 10}],10, AnimationRunning -> False]$

Mathematica code:

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
     ImageResize[ImageTake[ImageCrop[
       DensityPlot[
         Sin[104.54*Abs[(x + I y)^2]], 
       {x, -2.5, 2.5}, {y, -2.5, 2.5}, PlotPoints -> 27, 
       Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834],
     800], {100 + t, 700 + t}, {100 - t, 700 - t}],{500, 500}],
    f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
 {t, 0, 90, 10}],
10, AnimationRunning -> False]

Notes: 243 3/26/12 — 8:30pm Filed under: #GIF #Mathematica #logpolar coordinates #density plot #PS

$High-res: 800x800 Mathematica code: f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}ImageTransformation[ ImageCrop[ DensityPlot[ Sin[104.54*Abs[(x + I y)^2]], {x, -2.5, 2.5}, {y, -2.5, 2.5}, PlotPoints -> 27, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800],f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]$

High-res: 800x800

Mathematica code:

f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}

ImageTransformation[
 ImageCrop[
    DensityPlot[
       Sin[104.54*Abs[(x + I y)^2]], 
    {x, -2.5, 2.5}, {y, -2.5, 2.5}, 
    PlotPoints -> 27, Mesh -> False, Frame -> False, 
    ColorFunction -> Hue, ImageSize -> 834],
 800],
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]

High-res Notes: 82 3/26/12 — 6:00pm Filed under: #Mathematica #logpolar coordinates #density plot

$Mathematica code: f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}ListAnimate[ Table[ ImageTransformation[ ImageResize[ImageTake[ImageCrop[ DensityPlot[ Sin[84.74*Abs[(x + I y)^2]], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 35, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800], {119 + t, 683 + t}, {189 - t, 753 - t}],{500, 500}], f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], {t, 65, 0, 5}],10, AnimationRunning -> False]$

Mathematica code:

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
     ImageResize[ImageTake[ImageCrop[
       DensityPlot[
         Sin[84.74*Abs[(x + I y)^2]], 
       {x, -10, 10}, {y, -10, 10}, PlotPoints -> 35, 
       Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834],
    800], {119 + t, 683 + t}, {189 - t, 753 - t}],{500, 500}],
   f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
 {t, 65, 0, 5}],
10, AnimationRunning -> False]

Notes: 487 3/25/12 — 6:00pm Filed under: #GIF #Mathematica #form constants #logpolar coordinates #density plot

$High-res: 800x800 Mathematica code: f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}ImageTransformation[ ImageCrop[ DensityPlot[ Sin[84.74*Abs[(x + I y)^2]], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 35, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800],f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]$

High-res: 800x800

Mathematica code:

f[x_, y_] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}

ImageTransformation[
 ImageCrop[
   DensityPlot[
     Sin[84.74*Abs[(x + I y)^2]], 
   {x, -10, 10}, {y, -10, 10}, 
   PlotPoints -> 35, Mesh -> False, Frame -> False, 
   ColorFunction -> Hue, ImageSize -> 834],
 800],
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]

High-res Notes: 7 3/25/12 — 5:31pm Filed under: #Mathematica #density plot #logpolar coordinates #form constants

$High-res: 800x800 Mathematica code: ImageCrop[ DensityPlot[ Sin[84.74*Abs[(x + I y)^2]], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 35, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 944],800]$

High-res: 800x800

Mathematica code:

ImageCrop[
  DensityPlot[
    Sin[84.74*Abs[(x + I y)^2]], 
  {x, -10, 10}, {y, -10, 10}, 
  PlotPoints -> 35, Mesh -> False, Frame -> False, 
  ColorFunction -> Hue, ImageSize -> 944],
800]

High-res Notes: 8 3/25/12 — 5:00pm Filed under: #Mathematica #density plot

Type 2) form constant: spiral

Mathematica code:

Diagonals[t_] :=
 ImageCrop[
   DensityPlot[
     Cos[x + y - t*Pi/5],
   {x, -20 Pi, 20 Pi}, {y, -20 Pi, 20 Pi},
   PlotPoints -> 100, Mesh -> False, Frame -> False, 
   ColorFunction -> GrayLevel, ImageSize -> 522],
 500]

ListAnimate[
  Table[
   Diagonals[t],
  {t, 0, .9, .1}]]

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
      Diagonals[t],
    f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
  {t, 0, .9, .1}]]

Notes: 29 3/22/12 — 6:02pm Filed under: #GIF #Mathematica #form constants #logpolar coordinates #density plot

Type 1) form constant: rays

Mathematica code:

HStripes[t_] :=
 ImageCrop[
   DensityPlot[
     Cos[y - t*Pi/5],
   {x, -20 Pi, 20 Pi}, {y, -20 Pi, 20 Pi},
   PlotPoints -> 100, Mesh -> False, Frame -> False, 
   ColorFunction -> GrayLevel, ImageSize -> 522],
 500]

ListAnimate[
  Table[
   HStripes[t],
  {t, 0, .9, .1}]]

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
      HStripes[t],
    f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
  {t, 0, .9, .1}]]

Notes: 30 3/22/12 — 5:31pm Filed under: #GIF #Mathematica #form constants #logpolar coordinates #density plot

Type 1) form constant: tunnel

Mathematica code:

VStripes[t_] :=
 ImageCrop[
   DensityPlot[
     Cos[x - t*Pi/5],
   {x, -20 Pi, 20 Pi}, {y, -20 Pi, 20 Pi},
   PlotPoints -> 100, Mesh -> False, Frame -> False, 
   ColorFunction -> GrayLevel, ImageSize -> 522],
 500]

ListAnimate[
  Table[
   VStripes[t],
  {t, 0, .9, .1}]]

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]}

ListAnimate[
  Table[
    ImageTransformation[
      VStripes[t],
    f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}],
  {t, 0, .9, .1}]]

Notes: 339 3/22/12 — 5:00pm Filed under: #GIF #Mathematica #form constants #logpolar coordinates #density plot #circles

High-res: 800x800

Mathematica code:

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} 

honeycomb :=
 ImageCrop[
  DensityPlot[
    Sum[Cos[(Cos[n*2*Pi/6] + Sin[n*2*Pi/6])*x + (Cos[n*2*Pi/6] - Sin[n*2*Pi/6])*y], 
    {n, 0, 5, 1}], {x, -32 Pi, 32 Pi}, {y, -32.975 Pi, 32.975 Pi}, 
  PlotPoints -> 100, Mesh -> False, Frame -> False, 
  ColorFunction -> GrayLevel, ImageSize -> 834],
 800]

honeycomb

ImageTransformation[
 honeycomb,
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]

Notes: 27 3/14/12 — 6:10pm Filed under: #Mathematica #density plot #form constants #logpolar coordinates

High-res: 800x800

Mathematica code:

f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} 

checkergrid :=
ImageCrop[
  DensityPlot[
   Sum[Cos[(Cos[n*2*Pi/4] + Sin[n*2*Pi/4])*x + (Cos[n*2*Pi/4] - Sin[n*2*Pi/4])*y], 
   {n, 0, 3, 1}], {x, -32 Pi, 32 Pi}, {y, -32 Pi, 32 Pi}, 
  PlotPoints -> 100, Mesh -> False, Frame -> False, ColorFunction -> GrayLevel, ImageSize -> 834],
 800]

checkergrid

ImageTransformation[
 checkergrid,
f[#[[1]], #[[2]]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}]

Notes: 37 3/14/12 — 5:31pm Filed under: #Mathematica #density plot #form constants #logpolar coordinates

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