It is posted with his consent in the hope of stimulating students to look into math and physics.

#!/usr/bin/perl
use PDL;
use PDL::Graphics::TriD;
use PDL::Math; 

# electron simulation by Mark Baker

nokeeptwiddling3d;

 for $c(1..199999){
 
   $n = 6.28*$c; 
   $x = $c*rvals((zeros(9000))*$c);

   $cz = -1**$x*$c;
   $cy = -1**$x*sin$x*$c;
   $cx = -1**$c*rvals($x)*$c;

   $w = $cz-$cy-$cx;

   $g = sin($w);
   $r = cos($cy+$c+$cz);
   $b = cos($w);

   $i = ($cz-$cx-$cy);
   $q = $i*$n;
 
points3d [ $b*sin($q), $r*cos($q), $g*sin$q], [$g,$b,$r]; 

}

=head1

 Mark Baker's text references, and equation explanations:

   The book that I used to create the Piddle comes from 
   Rodger Penrose's book "The Road to Reality"

   From pages 562-564:
   We see the topic on 22.11 Spherical harmonics.
   We see that we can get the Cartesian coordinates for the equation

   [eq.1]

    x = sin [angle] cos [measure of longitude and latitude]
    y= sin [angle] sin [measure of longitude and latitude]
    z = cos [angle]

   this is how I came up with the Spherical harmonic dynamic equation 
   from the electron piddle ...


   [eq.2]

    $g = sin($w=$cz-$cy-$cx);
    $r = cos($cy+$c+$cz);
    $b = cos($w);

    Now this is not the same equation as above , but it does help 
    us to see the [inner magnetic field] and the [outer electric field
+] 
    in a Spherical Harmonic Dynamical Geometry , which was my main con
+cern...

   
   Dissecting the equation further we have :

    A equation I got from the book "Fundamental Formulas of Physics"
    edited by Donald H. Menzel a Director at the Harvard Collage Obser
+vatory
    page 7 Volume 1

   [eq.3]

   [a] sin [2*pi*frequency] [time] + [b] sin [2*pi*frequency] [time] =
+ [c] sin([2*pi*frequency] [time] + [phase])  


   which is where the transformation below [eq.4] came from me trying 
+to put the above [eq.3] 
   equation in  Cartesian coordinates that worked with the equation [e
+q.2] from [eq.1] ...

   [eq.4]

    $cz = -1**$x*$c;
    $cy = -1**$x*sin$x*$c;
    $cx = -1**$c*rvals($x)*$c;

   ------------------------------------

   So looking at the full piddle we have :

 
   for $c(1..99){ ## here c acts like the [2*pi* frequency] from  [eq.
+3]

   $n=6.28*$c; ## which is realized here 

   $x=$c*rvals((zeros(9000))*$c); ## some PDL minipulation 

   $cz = -1**$x*$c; ## a further transformation [eq.3]
   $cy = -1**$x*sin$x*$c;
   $cx = -1**$c*rvals($x)*$c;


   $g = sin($w=$cz-$cy-$cx);  ## a transformation of [eq.1] 
   $r = cos($cy+$c+$cz);      ## the main Geometry that ties together 
   $b = cos($w);              ## the transformation of [eq.4]


   $i=($cz-$cx-$cy); ## additional Geometry needed 

   $q=$i*$n;

   points3d[ $b*sin($q), $r*cos($q), $g*sin($q)], [$g,$b,$r] } ## furt
+her transformation that makes every thing work 

=cut
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