> with(plots,polygonplot3d,display3d):
# CantorSequence constructs a list containing the sequence p^i i=0, 1,
# ... N-1.  
# The value p should be less than 1/2.  CantorSequence(4,1/3) will
# construct
# the first four elements of the sequence used to construct the Cantory
# ternary set.
> CantorSequence := proc(N:integer,p)
> local i,lst:
> lst := []:
> for i from 0 to N-1 do
> lst := [op(lst),p^i]:
> od:
> lst:
> end:
# GraphPsiHat draws the approximation of the Cantor function on the 2D
# Cantor set 
# defined by the sequence cseq.  NOTE: unlike GraphPsiHat for the 1D
# sets, this version
# displays the graph.  GraphPsiHat(CantorSequence(6,1/3)); will display
# the graph of an
# approximation of the Cantor ternary function on the 2D ternary set.
> GraphPsiHat := proc(cseq:list)
> local n,k,k1,k2,crds,crds2,these,rect1,rect2,h,farbe:
> global all,plotme:
> all := []:
> crds := [0,1]:
> for n from 2 to nops(cseq) do
> crds2 := []:
> these := []:
> for k from 0 to nops(crds)/2-1 do
> crds2 :=
> [op(crds2),crds[2*k+1],crds[2*k+1]+cseq[n],crds[2*k+2]-cseq[n],crds[2*
> k+2]]:
> these := [op(these),
> [crds[2*k+1],crds[2*k+1]+cseq[n],crds[2*k+2]-cseq[n],crds[2*k+2]] ]:
> od:
> crds := crds2:
> for k1 from 1  to nops(these) do
> for k2 from 1 to nops(these) do
> h := ((2*k1-1)/2^(n-1)+(2*k2-1)/2^(n-1))/2:
> all := [op(all), [ h,these[k1],these[k2] ]]:
> od:
> od:
> od:
> plotme := {}: 
> for n from 1 to nops(all) do
> farbe := COLOUR(RGB,1,op(1,all[n]),op(1,all[n])):
> rect1 := [
> [all[n][2][2],all[n][3][1],all[n][1]],[all[n][2][3],all[n][3][1],all[n
> ][1]],[all[n][2][3],all[n][3][4],all[n][1]],[all[n][2][2],all[n][3][4]
> ,all[n][1]] ]:
> rect2 := [
> [all[n][2][1],all[n][3][2],all[n][1]],[all[n][2][4],all[n][3][2],all[n
> ][1]],[all[n][2][4],all[n][3][3],all[n][1]],[all[n][2][1],all[n][3][3]
> ,all[n][1]] ]:
> plotme := plotme union {polygonplot3d(rect1,color=farbe,style=patch),
> polygonplot3d(rect2,color=farbe,style=patch) }:
> od:
> display3d(plotme):
> end:
# Display an approximation of the Cantor function on the 2D ternary set
> GraphPsiHat(CantorSequence(3,1/3));
>