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        • The Effect of Prozac on the Brain
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        • Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons
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        • Dictyostelium Discoideum
        • The Future of Solar Cell Technology
        • And Many More...
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        • Alternative Energy Sources, New but Unused
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        • The Current State of American Education
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        • Interview With an Architect
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        • Missing from Science Class
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FRACTALS IN NATURE

Editor's note: Sasha M. ('17) explores the concept of geometric fractals.
A fractal can be both a natural phenomena and a mathematical set that shows a repeating pattern. These patterns are complex and reoccur over different scales. The same type of structure must appear of all scales. The existence of what we now know as fractals began with the notion of recursion, which made fractals constantly changing systems. They go on forever, connecting to the idea of unpredictability, or the chaos theory. But these patterns aren’t completely alien to us, since they are often seen in nature.

Fractal problems that we learn about in math classes are called geometric fractals. The problems start with a shape called the initiator and all the subparts of that shape are called the generators. With each new generator, the length of each segment increases by its scaling factor, getting closer and closer to infinity. This also makes the perimeter of fractal infinity. Based on the number of sides the shape has, a fractal dimension (or equation) of a shape can be written using its scaling factor.

The most common demonstration self-similarity and fractals exist in nature. Leaves, ferns, clouds, mountains, lighting, snowflakes, and more all are examples of fractals. One of the famous earliest types of fractals is called the Koch Snowflake Fractal. It starts off with an equilateral triangle that is then divided into three equal sections. Coming out of each middle section, another equilateral triangle is formed. This continues on forever. Niels Koch, a Swedish mathematician, first discovered this fractal in 1904. It was defined as a fractal, because no matter what scale you looked at the fractal, it is that the shape will look the same. Though it has an infinite perimeter, it has a finite area.

In computer graphics fractals are helpful in correctly representing objects from nature. Primitive shapes are simple to express with 2D and 3D technology. For more complex images such as trees or clouds, the computer graphics industry is using fractal techniques to attempt to recreate these objects. There are a multiple ways that a series can behave. It can go into infinity, decrease to zero, move back and forth between numbers, or just not have a clear pattern. To model the nature in the world we live in, mathematicians and computer scientists create functions for each type of fractal and modify it to look a certain way. Fractals are now becoming a very important part of computer graphics.

Examples of Natural Fractals:

Examples of Computer-generated Fractals:

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  • Home
  • Who We Are
  • HOW TO SUBMIT
  • Past Publications
    • 2018 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Scientific Research
    • 2017 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Reactions and Responses
      • Scientific Research
    • 2016 Publication >
      • Historical and Current Explanations
      • Mathematic and Scientific Explorations
      • Scientific Research
      • Reactions and Responses
      • Artistic Creations
    • 2015 Publication >
      • Historical and Current Explanations >
        • Bell Curves
        • Birds Vs. Turbines
        • Energy in the Obama Era
        • The Future of Neuroscience
        • Gender Gap in Math
        • GMOs--Yes or No?
        • The History of Minecraft: How a Swedish Indie Game Came to Dominate the World
        • The Effect of Prozac on the Brain
        • Philae Lander's Discovery of Organic Molecules
        • Advantages and Disadvantages of Wind Turbines
        • Your Own Worst Enemy: An Overview of Lupus
        • The Methylhex Ban
        • The Effect of Lyme Disease on the Immune system
        • Infectious Mononucleosis
        • Replacing CFCs
        • The Switch
      • Mathematic and Scientific Explorations >
        • The 43rd Figure
        • The Clock
        • The Collatz Conjecture
        • Constructing a Soccer Ball
        • Determining how Ballparks Affect Batter's Ability to Create Hits
        • The Rotating Conundrum
        • Pythagorean Puzzle
        • Mathematic and Scientific Explorations
        • Kinetics Lab
        • Math in the Restaurant Business
        • Math as a Vessel for Social Change
        • Sustainability of Bottled Vs. Tap Water
        • Thoughts on the Lottery
        • Understanding Player Efficiency Rating
      • Scientific Research >
        • Communicating With Computers
        • The Mystery of Asthma
        • The Nanoscopic War Against Cancer
        • Phytochemistry
        • Solving the energy crisis with Intermediate Band Solar Cells
        • A Pain That Never Ends
        • Rapamycin Resistance
        • Ampacity of a Single Core Horizontal Cable
        • Morphological Properties of Texting Acronym Formation
        • cGAS and STING Expression
      • Reactions and Responses >
        • Can Humans Survive the Climate Crisis?
        • My Experience as a Teacher's Assistant
        • Ted Talk Responses
        • Teens For Food Justice
      • Artistic Creations >
        • Chandelier
        • Deltoidal Hexacontrahedon
        • Dodecahedron Card Trick
        • Eye of the Triangle
        • Free Radric Delantic Davis
        • The Grid
        • What Does A Randomly Composed Song Sound Like?
        • Science Wing Mural
    • 2014 Publication >
      • Cover Photo
      • Artistic Creations >
        • Art Using the Fibonacci Sequence
        • Computer Generated Architecture and Designs
        • Mathematical Landscape
        • Math Art
        • Math in Music
      • Historical and Current Explanations >
        • Algae Bio-Fuel
        • An Energy Alternative
        • Clean Energy In Transportation
        • Calorie Restriction
        • Creating Energy in the Modern World
        • Dietary Intervention Impact on Gut Microbial Gene Richness
        • Earthly Applications for NASA Technology
        • Explaining Relative Motion
        • Exploring Artificial Inteligence
        • Gamma Function
        • How Leaves Work
        • Hydrogen Fuel Cells
        • Music and Brain Development
        • Programming Calculators
        • The Science of Microsatellites
        • Sci-Fi Taser
        • Sloane's Gap
        • Sustainable Energy: Why Some Ideas Shine Brighter than Others
        • Understanding The Galvanic Cell
        • The Virus: Our Unforeseen Philosopher's Stone
        • What Are Fuel Cells and How Do They Work?
      • Mathematic and Scientific Explorations >
        • Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons
        • Big Bang
        • Dictyostelium Discoideum
        • The Future of Solar Cell Technology
        • And Many More...
      • Reactions and Responses >
        • Alternative Energy Sources, New but Unused
        • An Insight Into the Curious World of Ethnobotany
        • Challenging What We Think We Know
        • The Current State of American Education
        • Discovering New Numbers
        • Interview With an Architect
        • Life of Pi Response
        • Mathematical Art Video Commentary
        • Missing from Science Class
        • The Museum of Math
        • The Inside Scoop on a Real Mathematician
    • 2013 Publication
  • 2019 Publication
    • Scientific Research
    • Mathematical Exploration
    • Scientific Exploration
    • Computer Science