EXERCISE: Compute the similary dimension of the IFS attractors determined by the following parameters
a. q1, q2, q3,
b. q1 q3
c q1, q4, q5q1:=[3/4,0,0,3/4,0,0]:
q2:=[3/4,0,0,3/4,1/4,0]:
q3:=[3/4,0,0,3/4,0,1/4]:
q4:=[1/4,0,0,1/4,3/4,3/4]:
q5:=[1/4,0,0,1/4,1/4,0]:square:=[[0,0],[0,1],[1,1],[1,0]]:evalf(log(3)/log(1/(3/4)));polygonplot(final([square],[q1,q2,q3],11),color=green);in case a, the similarity dimension is 2.polygonplot(final([square],[q1,q3],11),color=green,scaling = constrained);In case b the similarity dimension is 1.polygonplot(final([square],[q1,q4,q5],9),color=green,scaling = constrained);With the tools we have, we cannot compute the similarity dimension.EXERCISE Find the IFS parameters of the following figure and compute the similarity dimension of the attractor.p1:=[1/4,0,0,1/4,0,0]:
p2:=[1/4,0,0,1/4,0,1]:
p3:=[1/2,0,0,1/2,1,0]:
p4:=[1/2,0,0,1/2,1,1]:
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(final([square],[p1,p2,p3,p4],6),color=yellow);fsolve((1/4)^d+(1/4)^d+(1/2)^d+(1/2)^d=1,d);The above is an approximation of the similarity dimension.EXERCISE Find the IFS parameters of the following figure and compute the similarity dimension of the attractor.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:=[0.4 ,0,0,0.2, 0,0.1]:
w2:=[0.4 ,0,0,0.2, 0.5,0.6]:
w3:=[0.2 ,0,0,0.4, 0,0.5]:
w4:=[0.2 ,0,0,0.4, 0.6,0]:
polygonplot(final([square],[w1,w2,w3,w4],6),color=yellow);The contraction ratio of the above four transformations is 4. Then the dimension of the attractor islog(4)/log(1/0.4)QUESTION: What is the similarity dimension in this case?MiscelaneaBox counting dimensionIterated function systems "out" of the planeIFS "addresses"
IFS attractor as the "solution of a equation"L-systemsLevy's fractalWhat is the definition of a fractal? What determines one?In the project,: Describe your fractal, Find one (at least) decompositon in smaller, scaled pieces.PLEASE LET ME KNOW IF THERE IS ANY OF YOUR SUBMITTED HOMEWORKS THAT IS NOT GRADED.ALSO, REMEMBER TO NOTIFY ME IF YOU WANT TO SEE WHETHER YOUR PROJECT "WORKS' AS WRITTING REQUIREMENT.EXERCISE: Find the fractal determined by the following L-systemInitiator: a segment (NOTE: You can also find the IFS parameters of the figure as extra credit for the project.)Generator: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: You can also do the following exercise as extra credit for the project.EXERCISE:1. Write a procedure that takes as input a list of points, and a list of affine transformations and gives as output the result of applying all the transformation to all the points. 2. Write a procedure that takes as input a list of points, a list of affine transformations and and a positive integer n and gives the following output.a0. if n=0, the output is the original list of points.a1. if n=1, the output is the result of applying all the affine transformations to all the points.a2. if n=2, the output is the resutl of aplying all the affine transformations to all the points obtained in a1....In general, if n>1, then the ouput is the resutl of applying all the affine transformations to all the points obtained in the step n-1the step 3. Apply the procedure obtained in 2. to your favourite sets parameters of IFS.transformPoint:= proc(point , tr)
return [ tr[1]*point[1]+ tr[2]*point[2]+tr[5] , tr[3]*point[1]+ tr[4]*point[2]+tr[6] ]
end proc:transformPolygon:=proc(poly, tr)
return [seq( transformPoint(poly[i], tr), i=1..nops(poly))];
end proc:with(plots):listTrlistPol:=proc(listPol, listTr)
return seq( applyListToPoly(listPol[i], listTr), i = 1..nops(listPol));
end proc:applyListToPoly:=proc(poly, listTr)
return seq( transformPolygon( poly ,listTr[i] ) , i =1..nops(listTr) )
end proc:final := proc(listP, listT,n)
local x0, i:
x0:= listP:
for i from 1 to n do
x0:=[listTrlistPol(x0,listT)]:
end do;
return x0;
end proc:newCoord:=proc(a, r, e, f)
return [r*cos(a), -r*sin(a), r*sin(a), r*cos(a), e,f ];
end proc:Von koch curves parameterstr:=[[0,0],[1,0],[0.5,0.5]]:
t1:=newCoord(0,1/3,0,0):
t2:=newCoord(0,1/3,2/3,0):
t3:=newCoord(Pi/3,1/3,1/3,0):
h:= sqrt(3)/6:
t4:=newCoord(-Pi/3,1/3,0.5,h):
Sierpisnky carpett1:=[1/3,0,0,1/3,0,0]:
t2:=[1/3,0,0,1/3,1/3,0]:
t3:=[1/3,0,0,1/3,2/3,0]:
t4:=[1/3,0,0,1/3,2/3,1/3]:
t5:=[1/3,0,0,1/3,2/3,2/3]:
t6:=[1/3,0,0,1/3,1/3,2/3]:
t7:=[1/3,0,0,1/3,0,2/3]:
t8:=[1/3,0,0,1/3,0,1/3]:
IFS parameters of the Sierpinsky Gasketa:=[1/2,0,0,1/2,0,0]:
b:=[1/2,0,0,1/2,1/2,0]:
c:=[1/2,0,0,1/2,1/4,1/2]:
IFS parameters of the Cantor seta1:=[1/3,0,0,1/3,0,0]:
a2:=[1/3,0,0,1/3,2/3,0]:
EXERCISE Find the IFS parameters of the next 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