**Fractal or Fiction?**

What if I told you that you are a fractal? Of course, this is more theoretical than any of this presentation yet. Although extreme, the basis behind my hypothesis is similar. You are yourself, made of body and mind. Your physical self is made of organ systems working together so that you can function. Organs systems are made of organs, which are made of grouped tissue. Tissue is made of cells, which can be even farther broken down into organelles and what makes them up. The subatomic particles, protons, neutrons, and electrons, are smaller than an atom. The claim is that there is nothing smaller than a quark, which is what makes up subatomic particles. But how do we really know this? We learn new things in science everyday. Yes, it is assumed that there is nothing smaller. But then again, it was assumed that the earth was flat. Guess what? That was an incorrect assumption. We know nothing for sure of scientific discovery. This way of thinking can lead to wonder, so I won't go in depth on the idea of a phaneron. If you're a solipsist or not, bare with me.

Thoughts to Boggle the Mind

Of course, space and family trees don't show perfect uniformity to the definition of a fractal. These examples are more theoretical than definite. There have been articles upon articles written about these topics.

Theory at Work

Trees generally look like fractals, just like a bushel of broccoli does. Family trees can be viewed as fractals because of the multiplying of people. For example, my great-grandmother had two daughters. One daughter had one child, the other had eleven. These children of my great-grandmother's children had even more children. The generations multiplied the family's population by "branching off" into more and more people. Also, just a model of a family tree (like the one on the right) looks like a fractal.

The Family Tree

A fractal is a pattern that repeats itself on a smaller scale within its picture. A geometric term, it implies an infinite measure of a shape or object.

What is a Fractal?

Broccoli

Common Real-Life Fractals

The whole point of fractals is pattern in an infinite sense. There is no way to accurately measure the area or even perimeter of a fractal because its calculations cannot be fathomed. The ever-expanding sides cannot be measured precisely.

Think of the California Coastline. The side is not just a straight line. It is made up of indents of sand, rock, dirt, and other materials that we don't consider while measuring the coastline. It isn't really possible to calculate the exact length of it. This is because we A) don't have the measuring units small enough to evaluate this and B) if you look at the edge of California, you don't see just a line.

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When referring to fractals, Romanesco broccoli is usually shown as an example. However, any broccoli is a fractal. Some people refer to broccoli, saying it looks like a "mini tree". If you take a closer look, each branch on the broccoli looks like a "mini tree" as well. The broccoli branches off into the same shape multiple times.

{Snowflake}

Ferns

Trees

To Infinity and Beyond!

**What is the extent of fractals in our world and in space?**

**By Maya Shydlowski #29**

The Mandelbrot Set

Computer-Generated Stroke of Genius

The Mandelbrot set was created by Benoit Mandelbrot, hence its name. Mandelbrot was the first to discover and put a name to the fractal. The Mandelbrot Set is a fractal with multiple shapes in it, of course repeating within the picture. This is an example of a true fractal because it simply never ends. There have been videos created zooming into a portion of the pattern, however, it is impossible to find an end or to fully zoom into any fractal.

Sierpinski Triangle

The Sierpinski Triangle is a simple fractal, with only one shape that is repeated. A triangle is placed upside-down in the center of the original triangle. This creates more triangles, which can each go through the same process and create an infinite triangle fractal.

The Julia Sets

The Fractal Universe

How much do fractals actually appear in our universe?

Space is split up into galaxies. We base this theory off what we have explored through pattern and high-powered telescopes. These galaxies branch off into solar systems, which hold orbits of planets and stars. These planets hold a number of matter that is practically incomprehensible to man. My thoughts were that all this "branching off" and large astronomical orbits would look like a fractal. Theoretically, space can go on forever; we do not know the end of space itself, nor will we ever. The galaxies may not be exact replicas of our universe, but they share a "branching off" system that is common throughout space's grand orbitals.

Fractals are supposed to be identical replications of itself within its picture. You don't look and think and act exactly like your mom, dad, grandma, or grandpa, but there are these magnificent things called genes. Genes allow you to look like and work like your ancestors. So the identical part of a fractal is just being stretched a bit in saying that you are similar, but not quite congruent to your elder family members.

Fractals can be seen in everyday life, from the simple fern to the complex human body. So, what

is

the extent of fractals in the world?

MITK12Videos, http://m.youtube.com/watch?v=XwWyTts06tU, Uploaded December 11 of 2012, time spent researching: about 10 minutes

Discovery, http://science.howstuffworks.com/fractal-pictures.htm#page=1, February 2011, time spent researching: 20 minutes

Prof. Dr. Joachim P. Spatz– Max Planck Institute for Intelligent Systems, Stuttgart site, Stuttgart, https://www.mpg.de/7647926/cancer_cell_fractal , December 05, 2013, time spent: 10 minutes

Colin Hill, http://www.fractaluniverse.org/v2/?page_id=76, September 2009, time spent: 45 minutes

fractalmath, http://m.youtube.com/watch?v=8ma6cV6fw24, uploaded July 10 of 2009, time spent: 20 minutes

Collins English Dictionary, http://dictionary.reference.com/browse/Fractal?s=t, © 2009, time spent: 5 minutes

Fractal Foundation, http://fractalfoundation.org/resources/what-are-fractals/, 2009, time spent: 10 minutes

Michael Sauce (Vsauce), http://m.youtube.com/watch?v=L45Q1_psDqk, June 3 of 2013, time spent: 30 minutes

TheHostPros, http://www.rense.com/general72/size.htm, June 22 of 2006, time spent: 5 minutes

Science Buddies, http://www.sciencebuddies.org/science-fair-projects/search.shtml?v=ia&ia=Math&p=5, ©2002, time spent: two hours

Bibliography

Thank You!