# Remove strange line in animation

Posted 7 years ago
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 Hello, I am trying to run some animation from intothecontinuum-blog, and in 2 animations I got a little problem, this here for example: SquareLattice[t_] := Graphics[{Table[ Rectangle[{i + t, j + t}], {i, -2, 42, 2}, {j, -2, 42, 2}], Table[Rectangle[{i + 1 + t, j + 1 + t}], {i, -2, 42, 2}, {j, -2, 42, 2}]}, PlotRange -> {{0, 40}, {0, 40}}, ImageSize -> 500] f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} ListAnimate[ Table[ImageTransformation[SquareLattice[t], f[#[], #[]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], {t, 0, .9, .1}]] The gif in the blog seems to be fine, but if I evaluate the code, I got a thin line on the left (I try to attach a picture). This phenomen I already have recognized in another animation....but why is it there? Whatever I try, I am not able to get it away...does anyone have a little hint for me how to remove it?Many thanks already! 13 Replies
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Posted 7 years ago
 Why does that line exist?Look at the Plot of ArcTan[x, y], which defines how the y coordinate is obtained: Plot3D[ArcTan[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}] There is a discontinuity where that line exists in your image. I imagine it has some numerical difficultly there.
Posted 7 years ago
 I think the real answer here is to do it differently, to avoid this. Why not make Parts of annuluses yourself? I spent a few minutes to get this: ClearAll[DashedCircle] DashedCircle[rs:{ri_,ro_},n_Integer,\[Theta]_:0]:=Annulus[{0,0},rs,#+\[Theta]]&/@Partition[Subdivide[0,2\[Pi],2n],2] L={0.1,100,40}; M=20; \[Lambda]=PowerRange[#1,#2,(#2/#1)^(1/#3)]&@@L; \[Lambda]=Partition[\[Lambda],2,1]; Graphics[MapThread[DashedCircle[#1,M,#2 \[Pi]/M]&,{\[Lambda],Mod[Range[Length[\[Lambda]]],2,0]}]] Giving: Adding the motion should not be too hard, I will leave that as an exercise... Perhaps you could just set the PlotRange slightly different each time to zoom in...
Posted 7 years ago
 Related Mathematica.SE thread: "How can this type of optical illusion be created in Mathematica?"This thread contains some other methods allowing creation of such figures.
Posted 7 years ago
 Very interesting, many thanks....but if I try  tile := Module[{KeyHole}, KeyHole[base_] := Sequence[Disk[{0, 1/3} + base, 1/10], Rectangle[{-1/30, 1/15} + base, {1/30, 1/3} + base]]; Image@ Rasterize@ Graphics[{Orange, Rectangle[{0, 0}, {1, 1}], Blue, Rectangle[{0, 0}, {1/2, 1/2}], Rectangle[{1/2, 1/2}, {1, 1}], Black, KeyHole[{0, 0}], KeyHole[{1/2, 1/2}], KeyHole[{1, 0}], White, KeyHole[{0, 1/2}], KeyHole[{1/2, 0}], KeyHole[{1, 1/2}]}, PlotRange -> {{0, 1}, {0, 1}}]] floortex := ImagePad[ImageRotate[#, Right], 5 First@ImageDimensions[#], "Periodic"] &[tile] LogPolar[{x_, y_}] := {Log[Sqrt[x^2 + y^2]], ArcTan[x, y]}; ImageTransformation[floortex, LogPolar, PlotRange -> {{-1, 1}, {-1, 1}}, DataRange -> {{-2 \[Pi], 0}, {-\[Pi], \[Pi]}}, Padding -> White] for example, I get the same problem. A visible white line on the left.... Seems I need to try one of the other ways shown.....(but as I read there, they-re up to 9 times slower....and the Raspberry already is very slow!).
Posted 7 years ago
 Many thanks, I'll play around with it when the other animation I am waiting for is ready...and post it here when I have had success, and how (but I think this will take a few days cause the actual one stopped today as a reason of insufficent memory...started it again with a change some hours ago...Raspberry isn't the fastest :) )
Posted 7 years ago
 Perhaps set \$HistoryLength = 2 so it doesn't save all the intermediate steps. In Mathematica the default is infinity. So it saves all the output, which you can access by Out, Out... or %, %%, %%% et cetera.
Posted 7 years ago
 Thanks, but does it make a difference if I only load a small codesnippet and evaluate it? Does it affect evaluation anyhow? Look like it is only relevant for the notebook to me / useless for me in view of memoryusage in an evaluation.
Posted 7 years ago
 Unless you use %, %%, %%% or Out[...] a lot, it has no difference, it just only saves the last n outputs instead of everything!
Posted 7 years ago
 This ClearAll[DashedCircle] DashedCircle[rs:{ri_,ro_},n_Integer,\[Theta]_:0]:=Annulus[{0,0},rs,#+\[Theta]]&/@Partition[Subdivide[0,2\[Pi],2n],2] L={0.1,100,40}; M=20; \[Lambda]=PowerRange[#1,#2,(#2/#1)^(1/#3)]&@@L; \[Lambda]=Partition[\[Lambda],2,1]; Graphics[MapThread[DashedCircle[#1,M,#2 \[Pi]/M]&,{\[Lambda],Mod[Range[Length[\[Lambda]]],2,0]}]] result in lots of "Subdivide is not a Graphics primitive or directive"-errors here...Regarding my first post SquareLattice[t_] := Graphics[{Table[ Rectangle[{i + t, j + t}], {i, -2, 42, 2}, {j, -2, 42, 2}], Table[Rectangle[{i + 1 + t, j + 1 + t}], {i, -2, 42, 2}, {j, -2, 42, 2}]}, PlotRange -> {{0, 40}, {0, 40}}, ImageSize -> 500] f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} ListAnimate[ Table[ImageTransformation[SquareLattice[t], f[#[], #[]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], {t, 0, .9, .1}]] and Why does that line exist?Look at the Plot of ArcTan[x, y], which defines how the y coordinate is obtained:Plot3D[ArcTan[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}] There is a discontinuity where that line exists in your image. I imagine it has some numerical difficultly there. I found out, that Plot3D[ArcTan[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}] seems not to be part of the correct code. What I've not found is a solution...the ready animation included in the .CDF-file available there (Link) seems to be fine - but if I evaluate it in Mathematica by myself, I'll get that line......
Posted 7 years ago
 Regarding the error; what version of Mathematica do you have? This needs 10.2 or higher for the Annulus command.
Posted 7 years ago
 I am using 10 (or 10.1?) - the latest available for the Raspberry.Minutes ago I've tried the next one from that blog, VHStripes[t_] := Graphics[{Thickness[.01], Line[Table[{{j + t, 22 + t}, {j + t, -2 + t}}, {j, -2, 22, 1}]], Line[Table[{{22 + t, i + t}, {-2 + t, i + t}}, {i, -2, 22, 1}]]}, PlotRange -> {{-.5, 20.5}, {-.5, 20.5}}, ImageSize -> 500] f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} ListAnimate[ Table[ImageTransformation[VHStripes[t], f[#[], #[]] &, DataRange -> {{-Pi, Pi}, {-Pi, Pi}}], {t, 0, .9, .3}]] (with the same result) where  f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} seems to be neccessary - so I assume the general problem could only be in the DataRange -> {{-Pi, Pi}, {-Pi, Pi}} or am I missing something?The really strange thing for me is, that these 2 anims running fine in the blog and in the .cdf-file.....some other animations on the same blog have that problem visible, too - but not these 2 ones. Have the creators faked them? (Edit: And one example in Alexey Popkov's link some postings higher resulting in the same problem here)Strange stuff for a non-mathematician..........However, I'll try one of the other way shown. But it would be great if someone could explain this problem a bit more....I did not proof it, but I do not think that the guy who made these anims posted the answer in the link above, too. And 2 people posting something, which presumably worked for them - but not here?
Posted 7 years ago
 It is because it does resampling close to the x-line where there is a jump in the plane. Using ImageTransformations it will subsample and average and all kinds of things, to avoid this, you could set: VHStripes[t_]:=Graphics[Style[{Thickness[.01],Line[Table[{{j+t,22+t},{j+t,-2+t}},{j,-2,22,1}]],Line[Table[{{22+t,i+t},{-2+t,i+t}},{i,-2,22,1}]]},Antialiasing->False],PlotRange->{{-.5,20.5},{-.5,20.5}},ImageSize->500] f[x_,y_]:={Log[Sqrt[(x)^2+(y)^2]],ArcTan[x,y]} ListAnimate[Table[ImageTransformation[Rasterize[VHStripes[t],"Image"],f[#[],#[]]&,DataRange->{{-Pi,Pi},{-Pi,Pi}},Resampling->"NearestLeft"],{t,0,.9,.3}]] which works for me.
Posted 7 years ago
 Solved, thats it, you're awesome! Tried around without 'rasterize' and some resampling-options, but it only seems to work with 'Nearestleft' - but with bad quality. But when I do it with 'Rasterize', I am able to set better resamplng-options, too - without that annoying line! Very good, now I can do further experiments :)