RE : string to identifier

On 22.01.2012 01:39, laurent couraud wrote:
> You can also use eval_string from the package stringproc.
>
> Laurent.


Thx. It :
* removes upper/lower case switching
* removes one language from  code ( older code have used 3 languages : 
Maxima, Lisp and gnuplot. New code uses 2 languages : Maxima and gnuplot. )
Below is new code.

I think about making scene ( scene1, scene2 ....) in similar way to make 
code shorter ( I hope not obfuscated) and then use :
draw(scene1, scene2)

Old code and image is  here :
http://commons.wikimedia.org/wiki/File:Parabolic_critical_orbits.png
more description :
http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/parabolic

Please look also at :

Category:Images with Maxima CAS source code
http://commons.wikimedia.org/wiki/Category:Images_with_Maxima_CAS_source_code

Category:Created with Maxima (software)
http://commons.wikimedia.org/wiki/Category:Created_with_Maxima_%28software%29

Thx

Adam




============== newest code ==============

kill(all);



/* ---------- functions ---------------------- */

/* conformal map  from circle to cardioid ( boundary
  of period 1 component of Mandelbrot set */
F(w):=w/2-w*w/4;


/*
circle D={w:abs(w)=1 } where w=ToCircle(t,r)
t is angle in turns ; 1 turn = 360 degree = 2*Pi radians
r is a radius
*/
ToCircle(t,r):=r*%e^(%i*t*2*%pi);




/*

http://en.wikipedia.org/wiki/Complex_quadratic_polynomial
*/
f(z,c):=z*z+c $

GiveCriticalOrbit(c,iMax):=
    /*
    computes (without escape test)
    critical orbit (forward orbit of critical point )
    and saves it to the list for draw package */
block(
  [z,orbit,temp],
  z:0, /* first point = critical point z:0+0*%i */
  orbit:[[realpart(z),imagpart(z)]],
  for i:1 thru iMax step 1 do
         ( z:expand(f(z,c)),
           orbit:endcons([realpart(z),imagpart(z)],orbit)),

  return(orbit)
)$


/* find fixed point alfa , returns a list */
GiveFixed(c):=
(
  [z],
z:float(rectform((1-sqrt(1-4*c))/2)),
[[realpart(z),imagpart(z)]]
)$



GiveC(angle,radius):=
(
  [w],
  /* point of  unit circle   w:l(internalAngle,internalRadius); */
  w:ToCircle(angle,radius),  /* point of circle */
  float(rectform(F(w)))    /* point on boundary of period 1 component of 
Mandelbrot set */
)$



compile(all)$



/* ---------- constant ---------------------------*/
Numerator :1;
DenominatorMax :10;
InternalRadius:1;
iMax:500;


/* -------------- main ----------------- */



for Denominator:1 thru DenominatorMax step 1 do
(
  InternalAngle: Numerator/Denominator,
  c: GiveC(InternalAngle,InternalRadius),
   /*  */
  eval_string(concat("z",string(Denominator)))::GiveFixed(c),
  /* */
 
eval_string(concat("orbit",string(Denominator)))::GiveCriticalOrbit(c,iMax)
);




/*-----------------------------------------------------------------------*/
load(draw); /* ( interface to gnuplot ) by Mario Rodriguez Riotorto 
http://www.telefonica.net/web2/biomates */

draw(

     terminal  = screen,
     columns =5,
     file_name = "b",
     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] */

     gr2d(
         title= "1/1  ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	
         point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit1),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z1),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

  gr2d(
         title= " 1/2 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	
         point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* criitical orbit */
	color		  =red,
	points(orbit2),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z2),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

gr2d(
         title= " 1/3 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit3),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z3),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

gr2d(
         title= " 1/4 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit4),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z4),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),
gr2d(
         title= " 1/5 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit5),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z5),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

gr2d(
         title= "1/6  ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	
         point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit6),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z6),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

  gr2d(
         title= " 1/7 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	
         point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* criitical orbit */
	color		  =red,
	points(orbit7),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z7),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

gr2d(
         title= " 1/8 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit8),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z8),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),

gr2d(
         title= " 1/9 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit9),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z9),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         ),
gr2d(
         title= " 1/10 ",
	user_preamble = "set border 0;set nokey;set size square;set noxtics 
;set noytics;",
	point_type    = filled_circle,
	points_joined = false,
         point_size    = 0.7,
         /* critical orbit */
	color		  =red,
	points(orbit10),
         /* parabolic fixed point */
	color		  =black,
	point_size    = 1.4,
	points(z10),
         /* criitical point */
	color		  =blue,
	points([0],[0])
         )



  );