18
$\begingroup$

Consider the code

a = Table[BesselJ[i, x], {i, 0, 3}]
Plot[a, {x, 0, 20}, Axes -> False]

producing

enter image description here

I'd like to transform the plot into a circle. In other words, I'd like to wrap the plot around a circle.

I found PolarPlot[{1, 1 + 1/10 Sin[10 t]}, {t, 0, 2 Pi}] producing

enter image description here

which looks like a sin curve wrapped around the circle.

I know that the result would not be smooth closed, but no problem.

Improve this question
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3
  • 2
    $\begingroup$ c[x_] := Table[BesselJ[i, x], {i, 0, 3}]; PolarPlot[ 3 + # & /@ c[10 t], {t, 0, 2 Pi}] $\endgroup$
    – Dr. belisarius
    Oct 30, 2014 at 23:27
  • $\begingroup$ @belisarius, perfect! Since I'll use 4 colours to each graph, how to pass the colours to PolarPlot? I tried PlotStyle but no success. $\endgroup$
    – Sigur
    Oct 30, 2014 at 23:30
  • $\begingroup$ Why closing vote? $\endgroup$
    – Sigur
    Oct 31, 2014 at 14:15

2 Answers 2

Reset to default
20
$\begingroup$

Update

ticks[x1_, x2_] := {#/10 + π/2, #} & /@ 
  FindDivisions[{10 (x1 - π), 10 (x2 - π)}, 20]

funcs = Table[3 + BesselJ[i, 10 (x -π/2)], {i, 0, 3}];
PolarPlot[funcs // Evaluate, {x, -π/2, 3π/2}, 
    PolarAxes -> Automatic,
    PolarTicks -> {ticks[0, 2 π][[2 ;; -2]], Automatic}
] (*thanks @kguler 's and @rm-rf 's advice*)

enter image description here

Manipulate version

Manipulate[
 funcs = Table[a BesselJ[i, 10 (x -π/2)] + b, {i, 0, n}];
 PolarPlot[funcs // Evaluate, {x, -π/2, 3π/2},
  Axes -> False] , {{n, 4}, 1, 10}, {{a, 1}, 0, 3}, {{b, 3}, 1, 5},
 ControlType -> {Automatic, VerticalSlider, VerticalSlider},
 ControlPlacement -> { Top, Left, Left}]

enter image description here

Original

funcs = Table[3 + BesselJ[i, 10 x], {i, 0, 3}]
PolarPlot[Evaluate@funcs, {x, 0, 2 π}] (* thanks @kguler's advice *)

Blockquote

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5
  • $\begingroup$ FOr v9 you need to use PolarPlot[Evaluate@funcs, {x, 0, 2 \[Pi]}] to get separate colors. (+1) $\endgroup$
    – kglr
    Oct 30, 2014 at 23:40
  • $\begingroup$ Nice! I'm trying to plot my graphs on a symmetric range around zero (for example, {x,-10,10}) and then I'd like the middle part pointing to north, that is, f(0) onto the vertical axis. $\endgroup$
    – Sigur
    Oct 30, 2014 at 23:46
  • 1
    $\begingroup$ @Sigur Try this: PolarPlot[funcs /. x -> y - π/2 // Evaluate, {y, 3π/2, -π/2}] $\endgroup$
    – rm -rf ♦
    Oct 30, 2014 at 23:53
  • $\begingroup$ @rm-rf, thanks. It works. The constant circle was confusing me :) $\endgroup$
    – Sigur
    Oct 30, 2014 at 23:57
  • $\begingroup$ Well, if we change a little bit the domain we can do it symmetric from the north to the south. $\endgroup$
    – Sigur
    Oct 31, 2014 at 0:44
16
$\begingroup$ 
Composition[
   {#, Scale[#, {-1, 1}, {0, 0}]} &,
   Rotate[#, Pi/2, {0, 0}] &,
   First
   ] /@ Table[
   With[{root = FindRoot[D[BesselJ[i, x], x], {x, 100}][[1, 2]]},

    PolarPlot[{1 + BesselJ[i, t root/Pi]}, {t, 0, Pi}, 
     PlotStyle -> {Thick, Blend["AvocadoColors", i/15]}]
    ]
   , {i, 0, 15}] // 
 Graphics[#, ImageSize -> 500, Background -> Orange] &

enter image description here

Improve this answer
$\endgroup$
5
  • $\begingroup$ @JunhoLee I find yours better bacause it is shorter :) Thanks, well, one could probably argue about colors :P p.s. I like the gradient in background which isn't there :) $\endgroup$
    – Kuba ♦
    Oct 31, 2014 at 0:39
  • $\begingroup$ @Kuba, amazing. Very beautiful. Since I'm doing a logo, unfortunately I can not use yours. But thanks for some idea. $\endgroup$
    – Sigur
    Oct 31, 2014 at 0:41
  • 2
    $\begingroup$ Now I know how they designed Amidala's hair. $\endgroup$
    – Öskå
    Oct 31, 2014 at 1:10
  • $\begingroup$ @Öskå It's not easy to be hairdresser there days :P $\endgroup$
    – Kuba ♦
    Oct 31, 2014 at 1:13
  • 1
    $\begingroup$ @Kuba Not to mention how hat it was during Bessel's time-frame en.wikipedia.org/wiki/Friedrich_Bessel#mediaviewer/… $\endgroup$
    – Dr. belisarius
    Oct 31, 2014 at 3:21

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