/* Image is made using segments. Segment is a pair of points connected with line ( points_joined = true ). 

Point can be describe by :
* 2 real numbers, like : [0,1] which means  0 + 1*i 
* 1 complex numbers, like : i = 0 + 1*i


   Ergodic Theory and Dynamical Systems (1998), 18 : pp 739-758
    1998 Cambridge University Press
    Describing quadratic Cremer point polynomials by parabolic perturbations
   DAN ERIK KRARUP SØRENSEN 
example 2.4 

*/


kill(all);
remvalue(all);


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


GivePoints0(n,r):= points([[1/(2^(2*n)),   1], [1/(2^(2*n))  , 1-r*(1-1/(2^(2*n+1)))]])$
GivePoints1(n,r):= points([[1/(2^(2*n-1)), 0], [1/(2^(2*n-1)), r*(1-1/(2^(2*n)))]]  )$

compile(all )$

/* ----- constans and variables     --- */

nMax:100;
r:3/4;
p:[];   /* list with points object */
pp:[];  /* list of points objects  */

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

    /* pair or real numbers*/  /* complex points */
pp:[points([[0,0],[1,0]]),    /* [0,1] */
    points([[0,0],[0,1]] ) ,  /* [0,i] */
    points([[0,1],[1,1]] )]$  /* [i,1+i] */

for n:0 thru nMax step 1 do
(
 p:GivePoints0(n,r),
 pp:cons(p,pp)
)$

for n:1 thru nMax step 1 do
(
 p:GivePoints1(n,r),
 pp:cons(p,pp)
)$


/* ---------- draw image  ----------- */
load(draw);/* by Mario Rodríguez Riotorto  http://riotorto.users.sourceforge.net/gnuplot/index.html  */


draw2d(
 title     = concat("The intricated double comb for r=",string(r)), /*  */
 xrange        = [-0.2,1.2],
 yrange        = [-0.2,1.2],
 file_name = "double_comb",
 terminal      = svg,
 point_type = filled_circle,
 point_size = 0.1,
 points_joined = true, /* draws segments between points  */
 color         = "blue",
 pp )$