Can Mathematica Produce High-Quality Plots of Hermite Gaussian Polynomials?

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SUMMARY

This discussion focuses on generating high-quality plots of Hermite Gaussian polynomials using Mathematica. Users reported that their initial plots lacked the desired clarity and detail, similar to the high-resolution example provided from Wikimedia. A key recommendation is to enhance the plot quality by adjusting the PlotPoints option to 200 in the DensityPlot function. Additionally, users should consider the ImageResolution parameter when exporting plots to achieve better visual fidelity.

PREREQUISITES
  • Familiarity with Mathematica 12.0 plotting functions
  • Understanding of Hermite Gaussian polynomials
  • Knowledge of high-resolution image export techniques
  • Basic principles of density plots and 3D visualizations
NEXT STEPS
  • Research how to optimize DensityPlot settings in Mathematica
  • Explore the ImageResolution parameter for exporting high-quality images
  • Learn about advanced plotting techniques in Mathematica for better graphics
  • Investigate the mathematical properties of Hermite Gaussian polynomials for improved visual representation
USEFUL FOR

Mathematica users, mathematicians, and educators looking to create high-quality visualizations of mathematical functions, particularly those interested in polynomial representations and graphical optimization techniques.

hangainlover
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Homework Statement


Hello everyone,

I was trying to plot (density plot and 3d plot) Hermite Gaussian polynomials on Mathematica hoping the plot will be good enough to show patterns such as this link :
http://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Hermite-gaussian.png/800px-Hermite-gaussian.png

Yet, my plot on mathematica is very crude.

It follows the pattern so the function itself must be fine

I doubt this is the best I can do with mathematica..



Homework Equations



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The Attempt at a Solution



I plotted it and the image is nowhere near what I want..
 

Attachments

Physics news on Phys.org
Attached file viewable for people with mathematica access.

The kinds of plots in the wikimedia pic are hi-res projections - where the greyscale "whiteness" depends on the density in each area element. (Divides the volume into cubic prisms.)
 
Try adding
PlotPoints -> 200
to your DensityPlot and see if that provides the quality you are looking for.

When using Export you might also look at the effect of ImageResolution.

A general rule you might keep in mind that seems to be proven again and again.

If it takes about x time to get the mathematics mostly correct then it can often take between 2x and 10x MORE time to get the graphics to sort of look like the quality that desktop publishing has convinced everyone that they should be able to produce on their own and to get the graphics to look exactly like what you want can often take up to Infinityx more time.
 

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