Re: Fractals and Graph Theory

There are a lot of types of "graphs".
Digraphs or directed graphs are
what are used mostly in fractals of the IFS and L system type.
For example:
a->c
c->d
d->a
Matrix={{0,1,0},
{0,0,1},
{1,0,0}}
Characteristic polynomial=x^3-1
The fudge Flake IFS is based on this cyclotomic C3 rotation group.

Code generalized :
PRINT "input number 2 to 4"
INPUT m
PRINT "input -1 for fudge flake and 1 for second kind of fudge flake"
INPUT s
SET MODE "color"
SET WINDOW 0,1922,0,1066
SET COLOR MIX (1) 0,0, 0
SET BACKGROUND COLOR "white"
LET x=1
LET y=1
LET c=0
LET s1=400
LET s2 =(s1)*1066/1922
DIM a(25),b(25)
FOR i=1 to m
LET a(i)=cos(2*pi*i/m)
LET b(i)=sin(2*pi*i/m)
NEXT i
PRINT " GENERAL Fudge Flake I.F.S. "
PRINT " BY R.L.BAGULA 15 Sept. 2002© copy rights reserved"
RANDOMIZE
PRINT " M=";m
PRINT " S=";S
FOR n= 1 TO 2000000
LET c =RND
LET l=1+int(c*m)
LET x1=s*(a(l)*y+b(l)*x)/sqr(m)+a(l)
LET y1=(a(l)*x-b(l)*y)/sqr(m)+b(l)
LET x=x1
LET y=y1
SET COLOR 15+(255-15)*l/(1.5*m)
IF n>10 THEN PLOT 1922/2+s1*x,1066/2+s2*y
NEXT n
END


Nic wrote:

Dear all,

I've a question about fractals and graph theory.
Please accept my apologies since the question could seems trivial, but I'm new in fractal world and it makes sense for me.
Suppose I have the following very simple structure:
a--c--d
It is to say: element "a" related to element "c", element "c" related to element "d" (commutative relations).
Can this structure, iterated a certain number of times and completed with the necessary graphic parameters, be considered as a fractal and drawn with a fractal generator?
Please accept my apologies for the trouble.
Many thanks for the help.

Best,
Nic

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