Summary

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

You may select the license of your choice.

Maxima CAS source code

Software :

• Maxima CAS
  • draw package by by Mario Rodriguez Riotorto ^[1]
• gnuplot

Metaprogramming : scenes is a string which is used as an input for draw command

/* 
Adam Majewski
fraktal.republika.pl

*/

kill(all);
remvalue(all);


/* compute vectors at the given points  vector ([x,y], [dx,dy]) 
  vector([x,y], [dx,dy]) plots vector [dx,dy] with origin in [x,y]. 
*/


 

GiveCirclePoint(t):=rectform(%e^(%i*t*2*%pi)); /* gives point of unit circle for angle t in turns */



GiveVector(origin, target):=block(
 [x,y,dx,dy],
 x:realpart(origin),
 y:imagpart(origin),
 dx:realpart(target)-x,
 dy:imagpart(target)-y,
 vector([x,y],[dx,dy])
)$

GiveAttractingVector(origin):=GiveVector(origin, 0)$ /* from origin to 0 */
GiveRepellingVector(target):=GiveVector(0, target)$  /* from 0 to target */


GiveAttractingVectors(Denominator):=(
 [AttractingInternalAngles, AttractingCirclePoints,nMax],
 nMax:Denominator,
 AttractingInternalAngles:makelist(n/nMax ,n,1,nMax),
 AttractingCirclePoints:listify(map(GiveCirclePoint,AttractingInternalAngles )),
 listify(map(GiveAttractingVector,AttractingCirclePoints))
)$



GiveScene(sTitle, vector):=
gr2d(title= sTitle,
        user_preamble = "set border 0;set nokey;set size square;set noxtics ;set noytics;",
        yrange = [-1,1],
        xrange = [-1,1],
        [head_length=0.1, head_angle  = 10, color=blue],
        vector
        )$



compile(all);

/* ----------------*/




scenes:[];
for Denominator:1 thru 10 step 1 do
(
 
 scene:GiveScene(string(1/Denominator),GiveAttractingVectors(Denominator)),
 scenes:endcons(scene,scenes))$


/* ----------draw the vector field ----------------------------*/

draw(
     
 terminal  = 'svg,
    columns =5,
    file_name = "b", /* one can add path here */
    pic_width  = 1000,    /* Since Maxima 5.23, pic_width and pic_height are deprecated. */
    pic_height = 500,    /* See option dimensions. To get the same effect, write dimensions=[800,600] */
    scenes


)$
 
  

References

1. ↑ Draw package by Mario Rodriguez Riotorto for Maxima CAS