> with(plots,display):
# CantorSequence generates a list that contains the first N elements of
# the sequence
# p^i i=0, 1, . . .  The value p should be less than 1/2.
# CantorSequence(4,1/3) will generate the first four elements of the
# sequence used to
# construct the Cantor 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 graph of the Cantor function based on the
# sequence cseq
# in the color farbe.  cseq should be a list (such as those created by
# CantorSequence),
# and farbe should be a legitimate Maple color (e.g., red, blue,
# COLOR(RGB,.2,.2,.2)).
# GraphPsiHat(CantorSequence(4,1/3),red) will draw an approximation of
# the
# Cantor ternary function.
# NOTE: GraphPsiHat will return a plot object.  You must use display to
# view the graph.
> GraphPsiHat := proc(cseq:list,farbe)
> local n,k,crds,crds2:
> global all,all2:
> all := []:
> all2:={}:
> crds := [0,1]:
> for n from 2 to nops(cseq) do
> crds2 := []:
> 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]]:
> all := [op(all),
> [(2*(k+1)-1)/2^(n-1),crds[2*k+1]+cseq[n],crds[2*k+2]-cseq[n]] ]:
> od:
> crds := crds2:
> od:
> for k from 1 to nops(all) do
> all2 := all2 union
> {plot(op(1,all[k]),x=op(2,all[k])..op(3,all[k]),color=farbe)};
> od:
> all2:
> end:
# Draw a the Cantor ternary function in blue
> display(GraphPsiHat(CantorSequence(6,1/3),blue));
# Display four Cantor functions together.
> bild := []:
> for i from 0 to 3 do
> bild :=
> [op(bild),GraphPsiHat(CantorSequence(4,1/(3+i)),COLOR(RGB,i/3,0,(3-i)/
> 3))]:
> od:
> display(bild);
>