# The reason that the plot is not symmetrical after rotation [closed]

Now I am a little confused about the reason my plot seems to be not symmetrical. I believe the plot should like several circles while it is not. Here is my code. And the picture looks like this.

DensityPlot[BesselJ[1, Sqrt[x^2 + y^2]], {x, -20, 20}, {y, -20, 20},


And when I expand the region, it seems to be worse:

DensityPlot[BesselJ[1, Sqrt[x^2 + y^2]], {x, -200, 200}, {y, -200, 200},Mesh -> False] I wonder if anyone knows the reason why it looks like that?

## closed as off-topic by Bob Hanlon, m_goldberg, halirutan♦Jul 24 '18 at 13:30

This question appears to be off-topic. The users who voted to close gave this specific reason:

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## 2 Answers

The Bessel functions are highly oscillating and

DensityPlot[BesselJ[1, Sqrt[x^2 + y^2]], {x, -200, 200}, {y, -200, 200},
Mesh -> All] shows you that the triangle grid on which this is plotted is much too coarse. The grid cannot capture details, if the maximum edge length of each triangle is not smaller than "half the wavelength".

Try

DensityPlot[BesselJ[1, Sqrt[x^2 + y^2]], {x, -20, 20}, {y, -20, 20},
PlotPoints -> 100] For the second plot, the number of buckles within the plot range is so large that we have to crank up the PlotPoints even more:

DensityPlot[
BesselJ[1, Sqrt[x^2 + y^2]], {x, -200, 200}, {y, -200, 200},
Mesh -> None, PlotPoints -> 300] The documentation for DensityPlot states: Animate[
DensityPlot[
BesselJ[1, Sqrt[x^2 + y^2]]
, {x, -20, 20}
, {y, -20, 20}
, Mesh -> False
, PlotPoints -> k
, PlotLabel -> StringTemplate["PlotPoints->"][k]
]
, {k, 2, 50, 1}
] 