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Quiz about Fun With Fractals  A Quiz About Roughness
Quiz about Fun With Fractals  A Quiz About Roughness

Fun With Fractals - A Quiz About Roughness


Fractal are never-ending, infinitely complex patterns that are self-similar across different scales. Fractals are described as being "everywhere continuous but nowhere differentiable." Some just say they're pretty.

A multiple-choice quiz by havan_ironoak. Estimated time: 4 mins.
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Time
4 mins
Type
Multiple Choice
Quiz #
397,048
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
243
Last 3 plays: Guest 90 (1/10), Guest 1 (10/10), Guest 2 (9/10).
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Question 1 of 10
1. Fractals are closely related to and often considered part of what field of Mathematics?
Hint


Question 2 of 10
2. Fractal based equations have been found useful in all of these applications but one. Which? Hint


Question 3 of 10
3. What mathematician coined the word fractal and referred to himself on occasion as a "fractalist?" Hint


Question 4 of 10
4. Fractals have become much more popular since the advent of electronic computing because they depend upon what aspects of computing? Hint


Question 5 of 10
5. Which is these commonly used consumer devices makes applied use of fractals? Hint


Question 6 of 10
6. Which of the following is NOT a good example of how fractals appear in nature? Hint


Question 7 of 10
7. In 1904 one of the earliest & simplest fractals was described by Helge von Koch, the "Koch Snowflake."

This snowflake is based on what standard geometric shape?
Hint


Question 8 of 10
8. A slightly more complex fractal starts with an upright equilateral triangle and divides it into four equilateral triangles by connecting the midpoints of the three sides forming an upside down interior equilateral triangle.

Recursively performing this process for every resultant triangle produces a drawing that begins to look like a gasket. What is this fractal figure called?
Hint


Question 9 of 10
9. Benoit Mandelbrot started concentrating on fractals when he was asked to look into a problem that IBM was having. What did the problem concern? Hint


Question 10 of 10
10. Applying a set rules recursively to a particular problem occurs in several brain teaser games. Diagramming the shortest and longest solutions will sometimes result in figures that look uncannily like on of the fractals we've discussed. Which popular puzzles are an exemplar of that? Hint



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Quiz Answer Key and Fun Facts
1. Fractals are closely related to and often considered part of what field of Mathematics?

Answer: Geometry

Fractals are infinitely complex patterns that are self-similar across different scales The term "fractal" itself comes from the notion of breaking a line or a figure up into smaller but similar instances of the original. Conceptually, this is done over and over, ad-infinitum resulting in infinite sets.

Combinatorics deal primarily with counting and sets. Game theory deals primarily with strategies between rational decision makers (often in zero-sum games). Probability deals with the chances of indeterminate outcomes (e.g. odds & gambling)
2. Fractal based equations have been found useful in all of these applications but one. Which?

Answer: determining optimal pathing in highway traffic situations

Loren Carpenter of Pixar Studios used fractals on low speed computers to simulate mountain ranges when employed at Boeing and then again at Lucasfilm in developing the world's first fully CGI sequence for a feature film, "Star Trek II: The Wrath of Khan". Mandelbrot initially presented his work in a paper "How Long Is the Coast of Britain?." Repeated branching as in tress, the placement of leaves in ferns, and blood vessels in the circulatory system have all been successfully modeled using fractal functions.

Highway traffic problems don't involve the sames aspects of natural roughness in which fractals excel. They tend to be more related to probability.
3. What mathematician coined the word fractal and referred to himself on occasion as a "fractalist?"

Answer: Benoit Mandelbrot

Known for his talent for practical research, Mandelbrot and computer affinity, born a Polish Jew, became an IBM employee in 1958. He was one of the first to use computer graphics to create and display fractal geometric images which display "the art of roughness."
4. Fractals have become much more popular since the advent of electronic computing because they depend upon what aspects of computing?

Answer: all of these

Fractal problems have been touched upon since as early as the 17th century but most of the earliest work in the area was hindered by the amount of repetitive calculation that was required. In fact some of the earliest formulae in this area were referred to as mathematical "monsters" because of their unwieldiness.
5. Which is these commonly used consumer devices makes applied use of fractals?

Answer: cell phones

Most cell phones use antennas that are based on fractal designs. The recursive nature of self-similarity that is required of fractal values pretty much guarantee a wide variety of effective lengths meaning that they can handle a wide spectrum of signal frequencies in a smaller footprint than other antenna designs.
6. Which of the following is NOT a good example of how fractals appear in nature?

Answer: the stripes on a zebra

The stripes on a zebra are basically regular and mirror the growth patterns of grasses. If viewed in closer detail they do not exhibit the "self similar" aspect of fractals.

Conversely, zooming in on snowflakes, coastlines and tree branches all yield images that exhibit similarities to their zoomed out images.
7. In 1904 one of the earliest & simplest fractals was described by Helge von Koch, the "Koch Snowflake." This snowflake is based on what standard geometric shape?

Answer: an equilateral triangle

To construct a Koch snowflake, you need to do the following:

1) Start with an equilateral triangle.

2)Now divide each of the legs of that triangle into three equal parts and replace the middle third with two line segments of that length that form their own equilateral triangles (with no base), pointing outwards from the original shape.
This should be a six pointed shape similar to "the Star of David." Not that the perimeter of the resultant shape is 4/3rds the length of the original perimeter.

3) Dividing each of the resulting line segments into three parts and repeating
this process will yield a figure that has 18 points and begins to resemble a snowflake

4)The fourth iteration will yield a figure with 54 points, then 162, 486 and so on..

Each iteration yields a figure that has a perimeter 4/3s of the length of the previous figure and it quickly becomes apparent that, as iteration continues the perimeter will approach infinity even though the enclosed area remains finite.
8. A slightly more complex fractal starts with an upright equilateral triangle and divides it into four equilateral triangles by connecting the midpoints of the three sides forming an upside down interior equilateral triangle. Recursively performing this process for every resultant triangle produces a drawing that begins to look like a gasket. What is this fractal figure called?

Answer: the Sierpinski Triangle

The Sierpinski Triangle is also sometimes called the Sierpinski gasket or the Sierpinski sieve. It was first conceived by Wac³aw Sierpiñski in 1915. Though it's clearest when started with an equilateral triangle, other starting shapes can be used in this transformation. Most modern cell phone antennas are based on one of these types of functions.
9. Benoit Mandelbrot started concentrating on fractals when he was asked to look into a problem that IBM was having. What did the problem concern?

Answer: noise in incoming signal transmissions

Mandelbrot graphed the noise rate and noticed that the graphs looked almost identical regardless of the time scale. It reminded him of the self similarity that he'd heard about with "the monsters."
10. Applying a set rules recursively to a particular problem occurs in several brain teaser games. Diagramming the shortest and longest solutions will sometimes result in figures that look uncannily like on of the fractals we've discussed. Which popular puzzles are an exemplar of that?

Answer: Tower of Hanoi puzzle

In Tower of Hanoi puzzles the player must move disks from one rod to another one at a time subject to rules. In the standard version, each move must take only one disk from a stack and place it atop any other stack and no larger disk may be placed on top of a smaller disk.

In a full solution of this puzzle, each disk will move only half as often as the disk directly above it and plotting the movements by the height of the disk moved creates a fractal-like shape (although it would only be a true fractal for an infinite height puzzle).
Source: Author havan_ironoak

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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