Make each frame a seq of all previous frames

Carl Love — Fri, 08 Mar 2013 19:29:57 Z

The trick is to make each frame include a static (i.e. not insequence) display of all previous frames. This can be done with any animation. Here's the original code (which I indented) and my modifications. I added a splash of color. I also changed the sum to add for efficiency, which necessitated making g a procedure.

(***** begin original (comment out) *****
g:= sum(arctan(1/sqrt(n)), n = 1 .. i):
p:= seq(
   plots[polygonplot](
       [[0, 0],
       [sqrt(k+1)*cos(subs(i = k, g)), sqrt(k+1)*sin(subs(i = k, g))],
       [sqrt(k)*cos(subs(i = k-1, g)), sqrt(k)*sin(subs(i = k-1, g))]
       ], color = white
   ), k = 1 .. 70
):
plots[display]([p], insequence = true);
***** end original (comment out) *****)

N:= 70:
g:= k-> add(arctan(1/sqrt(n)), n= 1..k):
p:= [seq](
   plots:-polygonplot(
       [[0, 0], sqrt(k+1)*~[cos,sin](g(k)), sqrt(k)*~[cos,sin](g(k-1))
       ], color= COLOUR(HUE, k/N)
   ), k= 1..N
):
plots:-display([seq](plots:-display(p[1..K]), K= 1..N), insequence = true);

thanks Carl

brian bovril — Sun, 10 Mar 2013 16:44:17 Z

brilliant

MaplePrimes - answers and comments on Question, Spiral of Theodorus

Make each frame a seq of all previous frames

thanks Carl