Fractal geometry transcends the Euclidean dimensions in mind-blowing ways. Quantify your knowledge of fractals with this brain-bending quiz!

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Question 1 of 20

### When was the term "fractal" first used?

1871

1975

Though the pattern was noticed by artists early on in human history, and the mathematical core began to be formed in the 19th century, the term itself was not used until 1975.

1992

Question 2 of 20

### When a fractal produces the same shape at smaller and smaller scales, it demonstrates what?

Complexity

Self-similarity

Fractals are definitely redundant, and more than complex, but the property of self-similarity is their most defining characteristic.

Redundancy

Question 3 of 20

### Which fractal helped to calculate the length of the coastline of England?

Menger Sponge

Koch Snowflake

The Sponge and the Sausage would be useful if they could work as a yardstick, but the Koch Snowflake, with its progressively smaller "yardsticks," redefined the practice of measuring coastlines. Because of this, it's now generally acknowledged that any given coastline length needs to give the length of its yardstick in order to have real meaning.

London Sausage

Question 4 of 20

### The Mandelbrot Set is sums up the work of which mathematician?

Lewis Richardson

Georg Cantor

Gaston Julia

Gaston Julia developed the idea of the feedback loop, where the value produced by each iteration of a formula was recycled and used as the input value for the next iteration. Benoit Mandelbrot built on Julia's work and summed it up nicely with his Mandelbrot Set.

Question 5 of 20

### According to fractal geometry, the coastline of the United Kingdom is how long?

7,723 miles (12,429 kilometers)

infinite

The CIA World Factbook gives the coastline's length as around 7,723 miles, but Lewis Richardson, using the Koch Snowflake, realized that if you use a small enough ruler the coastline becomes infinite.

6,944 miles (11,175 kilometers)

Question 6 of 20

### If you wanted to simulate a mountain range using fractal geometry, what basic Euclidean shape would you want to use?

Square

Mountain shape

Triangle

If only mountain shapes were part of Euclidean geometry. Triangles work well in a pinch though, as Loren Carpenter found out working for Boeing in the late 1970s. He created an amazingly (for the time) realistic mountain range using computers a lot less powerful than the one in your cell phone.

Question 7 of 20

### In the fractal equation z = z2 + c, the variable c stands for what?

A real number

A complex number

In fact, it stands for two real numbers, as the variable c is what's called a "complex number." In this case, this number is a coordinate on the Cartesian Grid. By the way, Einstein also used this variable in his famous formula explaining the relationship of mass to energy, where c was the speed of light.

The speed of light

Question 8 of 20

### Mandelbrot coined the word "fractal" to explain what?

That fractal shapes can have non-integer dimensions

The term came about as a way to describe the fractional aspect of the dimension the shapes that became fractals were taking, since they defied description by traditional Euclidean terminology. Luckily for him, the artistic quality of fractals did wonders to help promote his efforts.

The fractured nature of fractal geometry

The fractious and chaotic aspect of fractals

Question 9 of 20

### Fractal dimension is a measure of what?

How many iterations it takes to create a shape

How far your mind has to bend to understand these things

How rough the surface of a shape is

For those brought up in traditional geometry it takes a little mind bending to reach outside of it. But fractal dimension provides a mathematical way to describe just how rough the surface of a shape is. The rougher the surface, the higher the dimension.

Question 10 of 20

### The Hausdorff-Besicovitch Dimension of a fractal is always:

Hard to say after a glass of wine

Less than its topological dimension

Greater than its topological dimension

One of the most important and mathematically rigorous ways to measure fractal dimension, the Hausdorff-Besicovitch Dimension is always greater than its correlated topological, or Euclidean, dimension. Mandelbrot once claimed that if Hausdorff is the father of non-standard dimension (which he is), then Besicovitch must be the mother. You get half credit if you answered A.

Question 11 of 20

### In a colorful version of a Mandelbrot Set, what do the colors represent?

Whatever the artist is trying to tell you

The value of z / log N

The speed at which the equation escapes towards infinity

Some artists definitely like fractals, but the colors are in fact representative of how fast the equation escapes the Mandelbrot Set to infinity. Each color represents one iteration, so the simplest Mandelbrot illustrations aren't very colorful. Throw in more and more and pretty soon you have a work of art.

Question 12 of 20

### What kind of fractal has been effectively used in telecommunications devices?

Julia Set

Dragon Curve

Menger Sponge

Telecommunications rely on the physical properties of radio waves, which like their name suggests travels in a wave-like way (think of a sine curve). This means that any antenna designed to pick up these waves should include wires that are equidistant from each other. The Menger Sponge achieves this property in a way that actually allows it to receive multiple wavelengths, making it ideal for for modern mobile devices.

Question 13 of 20

### What's the highest dimension a fractal can have?

One

Two

Three

Like real mountains and trees, fractals too have a limit of three dimensions. After that, you're off into a whole new world of space-time stuff.

Question 14 of 20

### What Japanese artist depicted fractal waves in his work "The Great Wave Off Kanagawa"?

Hiroshige

Tawaraya Sotatsu

Katsushika Hokusai

Most people couldn't name the artist, but they recognize the iconic work of Katsushika Hokusai, created in 1820. And you can even see Mount Fuji in the background.

Question 15 of 20

### What meteorologist first discovered the Butterfly Effect in 1960?

David Letterman

Carl-Gustaf Arvid Rossby

Edward Lorenz

Letterman was still studying algebra in junior high in 1960, but probably thinking more about television. Edward Lorenz wanted to re-run a weather prediction calculation, but shortened his input variable by a fraction of a percent, and was shocked when the end result was vastly different than before.

Question 16 of 20

### Why didn't Gaston Julia pursue his work with the Julia Set further?

He couldn't get funding.

He died before he could complete his work.

He didn't have a supercomputer.

You have to wonder how many great ideas suffered in the past umpteen thousand years for want of a good computer. In fact, the traditional meaning of "computer" was "one who computes." No wonder they didn't get very far.

Question 17 of 20

### Helge von Koche is best known for creating the Koch Snowflake, a fractal that illustrates what paradox?

An infinite perimeter with a dimension of zero

An infinite space surrounded by a finite perimeter

An infinite perimeter surrounding a finite space

It doesn't seem to make any sense when you say something has an infinite perimeter surrounding finite space, but you can't escape it. The weird thing is that it doesn't even converge toward a specific number. It's a true paradox. So next time something blurts out how long a coastline is (don't hold your breath), one-up them and ask them how long their yardstick is.

Question 18 of 20

### Which measure of fractal dimension utilizes the box counting method?

Hausdorff Dimension

Rényi Dimension

Minkowski-Bouligand Dimension

Some really hard-core mathematicians might cringe, but the Minkowski-Bouligand Dimension didn't bother Mandelbrot one bit. It's a fantastic and relatively simple way to get an idea of the fractal dimension of something, and it can be as accurate as you need. What more could you ask? Really hard-core mathematicians need not reply.

Question 19 of 20

### The Lorentz Butterfly is an example of what type of fractal?

Julia Set

Mandelbrot Set

Strange Attractor

This fractal and others like it get their beauty by flying around Strange Attractors, like a moon around its planet in some loopy orbit. Even the Julia and Mandelbrot sets are "attracted" to infinity to a certain degree, but apparently this is less strange to those naming these things.

Question 20 of 20

### Benoit Mandelbrot was born in what European country?

France

Belgium

Poland

At last, a little geography/history question. Although he spent most of his formative years in France, including a few years evading German occupiers on the prowl for Jews, he was born in Poland in 1924. Eventually, not finding his unconventional theories welcome among French academia, he joined IBM in America and discovered the wonderful abilities of computers.

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