(b) Determine the self-similarity dimension of the fractal.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b please
![1. Construction of a fractal: Begin with the line segment [0, 1] (the initiator). To obtain the
generator (the first iteration), replace the initiator with three line segments in a Z shape,
each segment scaled by a factor r = 1//3. The first segment is rotated 30° anticlockwise
with respect to the initiator. The middle segment makes an angle of 60° with the first
and last segments (see Figure below and the arrows to help with the orientation of the
segments). On each of the three new segments of the generator apply the same procedure
as for the initiator. Contimue applying this process infinitely often to obtain a (fractal)
curve.
609
60
(a) Sketch the second and third iteration in the above construction.
(b) Determine the self-similarity dimension of the fractal.
(c) Find the iterated function system (IFS) for the fractal curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af2e839-a835-4130-9203-42e58df89277%2F94d6003f-3bac-4d13-a9e9-1b900410e4d5%2Fsvbidr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Construction of a fractal: Begin with the line segment [0, 1] (the initiator). To obtain the
generator (the first iteration), replace the initiator with three line segments in a Z shape,
each segment scaled by a factor r = 1//3. The first segment is rotated 30° anticlockwise
with respect to the initiator. The middle segment makes an angle of 60° with the first
and last segments (see Figure below and the arrows to help with the orientation of the
segments). On each of the three new segments of the generator apply the same procedure
as for the initiator. Contimue applying this process infinitely often to obtain a (fractal)
curve.
609
60
(a) Sketch the second and third iteration in the above construction.
(b) Determine the self-similarity dimension of the fractal.
(c) Find the iterated function system (IFS) for the fractal curve.
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