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Mathematics
Date
Apr 3, 2024
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7
Uploaded by treyashmore
11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
1/7
Fractals Practice Due
Dec 1 at 11:59pm
Points
1
Questions
8
Available
until Dec 4 at 11:59pm
Time Limit
None
Allowed Attempts
Unlimited
Attempt History
Attempt
Time
Score
KEPT
Attempt 4
less than 1 minute
1 out of 1
LATEST
Attempt 4
less than 1 minute
1 out of 1
Attempt 3
less than 1 minute
0.13 out of 1
Attempt 2
2 minutes
0.87 out of 1
Attempt 1
16 minutes
0.83 out of 1
Correct answers are hidden.
Score for this attempt: 1
out of 1
Submitted Nov 29 at 8:51am
This attempt took less than 1 minute.
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0.13 / 0.13 pts
Question 1
Which of the following are reasonable definitions of a fractal?
Any object that displays self-similarity at all levels of magnification. Any object that's made up of several copies of smaller objects. Any object that's really complicated.
11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
2/7
Objects that show infinitely complex patterns that are self-similar across
different scales.
0.12 / 0.12 pts
Question 2
Here are the early stages of the Koch curve fractal.
Stage 1 has four line segments
Stage 2 has 16
line segments.
Stage 3 has 64
line segments.
Based on this pattern, Stage 4 will have 256
line
segments.
11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
3/7
Answer 1:
Answer 2:
Answer 3:
16
64
256
0.12 / 0.12 pts
Question 3
How many line segments will the Koch curve have at stage n
?
0.13 / 0.13 pts
Question 4
Which of these objects display self-similarity at different scales (even if it's
not infinite
self-similarity):
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11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
4/7
broccoli cupcake coastline of England fern a human foot a five pointed star 0.13 / 0.13 pts
Question 5
In this fractal, there is one copy of a picture which is reduced and inserted
into the big picture. Roughly what percent of the height of the big picture
is the height of the reduced picture? Answer with a decimal number, so if
the small picture is half as big, answer with 50. I have this one set to take
a range of reasonable answers.
11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
5/7
20
0.13 / 0.13 pts
Question 6
The Sierpinski Triangle can be viewed as three identical but reduced
copies of the entire figure. In other words, every triangular shape is made
up of three smaller triangular shapes in a pyramid configuration. What
fraction of the width is each sub-figure compared to the whole Sierpinski
triangle?
11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
6/7
1/2 1/3 1/8 Same width. 0.12 / 0.12 pts
Question 7
At stage 0, the Sierpinski triangle consists of a single, filled-in triangle. At
stage 1, there are three smaller, filled-in triangles. At stage 2, there are
9
filled-in triangles. At stage 3, there are
27
filled in triangles. At stage 4, there are
81
filled in triangles.
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11/29/23, 8:51 AM
Fractals Practice: Fa23 - MODERN MATHEMATICS: PLAN II (55330)
https://utexas.instructure.com/courses/1366856/quizzes/1840695
7/7
Answer 1:
Answer 2:
Answer 3:
9
27
81
0.12 / 0.12 pts
Question 8
How many filled-in triangles will there be at stage n
of the Sierpinski
triangle?
Quiz Score: 1
out of 1