English: This is a graph of the Mexican wavelet function in polar coordinates. It illustrates en:spontaneous symmetry breaking. It is intended to supersede File:Spontaneous symmetry breaking.jpg, which was tagged as a bad jpeg.

This is a surface of revolution obtained by rotating ${\displaystyle y=(x^{2}-1)^{2}}$ about the y axis.

The script for [:en:gnuplot] follows:

#!/usr/bin/gnuplot -persist
#
#    
#    	G N U P L O T
#    	Version 4.2 patchlevel 4 
#    	last modified Sep 2008
#    	System: Linux 2.6.28-15-generic
#    
#    	Copyright (C) 1986 - 1993, 1998, 2004, 2007, 2008
#    	Thomas Williams, Colin Kelley and many others
#    
#    	Type `help` to access the on-line reference manual.
#    	The gnuplot FAQ is available from http://www.gnuplot.info/faq/
#    
#    	Send bug reports and suggestions to <http://sourceforge.net/projects/gnuplot>
#    
# set terminal wxt 0
# set output
unset clip points
set clip one
unset clip two
set bar 1.000000
unset border
set xdata
set ydata
set zdata
set x2data
set y2data
set timefmt x "%d/%m/%y,%H:%M"
set timefmt y "%d/%m/%y,%H:%M"
set timefmt z "%d/%m/%y,%H:%M"
set timefmt x2 "%d/%m/%y,%H:%M"
set timefmt y2 "%d/%m/%y,%H:%M"
set timefmt cb "%d/%m/%y,%H:%M"
set boxwidth
set style fill  empty border
set style rectangle back fc lt -3 fillstyle  solid 1.00 border -1
set dummy x,y
set format x "% g"
set format y "% g"
set format x2 "% g"
set format y2 "% g"
set format z "% g"
set format cb "% g"
set angles radians
unset grid
set key title ""
unset key
unset label
unset arrow
set style increment default
unset style line
unset style arrow
set style histogram clustered gap 2 title  offset character 0, 0, 0
unset logscale
set offsets 0, 0, 0, 0
set pointsize 1
set encoding default
unset polar
unset parametric
unset decimalsign
set view 52, 253, 1, 1
set samples 40, 40
set isosamples 40, 40
set surface
set contour base
set clabel '%8.3g'
set mapping cartesian
set datafile separator whitespace
set hidden3d offset 0 trianglepattern 3 undefined 1 altdiagonal bentover
set cntrparam order 4
set cntrparam linear
set cntrparam levels incremental 0,1.4,1.4
set cntrparam points 5
set size ratio 0 1,1
set origin 0,0
set style data points
set style function lines
set xzeroaxis linetype -2 linewidth 1.000
set yzeroaxis linetype -2 linewidth 1.000
set zzeroaxis linetype -2 linewidth 1.000
set x2zeroaxis linetype -2 linewidth 1.000
set y2zeroaxis linetype -2 linewidth 1.000
set ticslevel 0.5
set mxtics default
set mytics default
set mztics default
set mx2tics default
set my2tics default
set mcbtics default
set noxtics
set noytics
set noztics
set nox2tics
set noy2tics
set cbtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
set cbtics autofreq 
set title "" 
set title  offset character 0, 0, 0 font "" norotate
set timestamp bottom 
set timestamp "" 
set timestamp  offset character 0, 0, 0 font "" norotate
set rrange [ * : * ] noreverse nowriteback  # (currently [0.00000:10.0000] )
set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
set xlabel "" 
set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
set x2label "" 
set x2label  offset character 0, 0, 0 font "" textcolor lt -1 norotate
set xrange [ -1.00000 : 1.00000 ] noreverse nowriteback
set x2range [ -3.29206 : 3.34697 ] noreverse nowriteback
set ylabel "" 
set ylabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by 90
set y2label "" 
set y2label  offset character 0, 0, 0 font "" textcolor lt -1 rotate by 90
set yrange [ -1.00000 : 1.00000 ] noreverse nowriteback
set y2range [ 853.321 : 878.574 ] noreverse nowriteback
set zlabel "" 
set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
set zrange [ * : 1.50000 ] noreverse nowriteback  # (currently [-1.80000:] )
set cblabel "" 
set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by 90
set cbrange [ * : * ] noreverse nowriteback  # (currently [-10.0000:10.0000] )
set zero 1e-08
set lmargin  -1
set bmargin  -1
set rmargin  -1
set tmargin  -1
set locale "C"
set pm3d explicit at s
set pm3d scansautomatic
set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB 
set palette rgbformulae 7, 5, 15
set colorbox default
set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 front bdefault
set loadpath 
set fontpath 
set fit noerrorvariables
set terminal svg
set parametric
set urange  [-pi:pi]
set vrange [0:1.25]
set xrange [*:*]
set yrange [*:*]
set zrange [*:*]
set hidden3d offset 1
set style line 1 lt rgb "black" lw 1
set style line 2 lt rgb "#bbbbbb" lw 1
splot cos(u)*v, sin(u)*v, (v**2 - 1 )**2 ls 1
# pause -1
#    EOF