The Mathematics of Bees, Bubbles, Platonic Solids, and Fractals (Repeating Self-Similar Pattern), U.S. Artist Jackson Pollock’s Artwork, and Computer Generated Imagery Animation Within Media: The Distance a Bee Must Fly to Produce 1 lbs of Honey, How Honeycombs are Structured, How Bees Routinely Manufacturer Honeycombs of the Same Size, the Ultimate Goal of Bees and Honeycombs, the Reason Bees Utilize Hexagons for Honeycombs, the Reason Bees Do Not Utilize Triangular or Rectilinear (Square) Honeycombs, the Most Efficient Shape for Storage, the Formulas to Calculate Space Utilization for Triangles, Squares, and Hexagons, the Thickness of Soap Bubbles vs the Thickness of Light, the Reason Soap Bubbles Produce Disparate Colors, the Ultimate Goal of Everything Within Nature, the Reason Soap Bubbles Are Spherical, the Reason Planets, Raindrops, and Volvox Plankton are Spherical, How Soap Bubbles Share Space and the Impact of Soap Bubbles Colliding With Eachother, the Location Geometry Takes Place as Soap Bubbles Are Combined, How the Geometry of Soap Bubbles Are Visualized, the Reason Soap Bubbles Revert to Become Spherical as Soap Bubbles Within Close Proximity Are Annihilated, the Angle All Walls Intersect Within a Soap Bubble, the 2 Dimensional Shape Soap Bubbles Create as They Combine, the Petrospheres (Carved Stone Balls) of Neolithic Scotland (10,000 B.C. – 2000 B.C.), the Largest Number of Faces Discovered Upon a Petrosphere, the Mathematical Concept Petrospheres Represented Throughout History, the Civilization Which Developed the Mathematical Subject of Geometry, the Person the Platonic Solids Are Named After, Ancient Greek Philosopher Aristocles’ (No Last Name) (Plato) (the Broad) View of the Platonic Solids, the Hypothesis of Why the Platonic Solids Were Developed, the Reason the Platonic Solids Work Well as Game Dice, the Only Shapes Which Allow for Equally Balanced Game Dice, How X-Ray Diffraction Helped Reveal the Atom, the Fallacy of Snowflakes Being Symmetrical, Snowflakes at the Molecular Scale vs Snowflakes at the Macroscopic Scale, the Reason Snowflakes Become Asymmetrical at the Macroscopic Scale, the Reason Snowflakes Become Complex Geometric Shapes, the Possibility of Discovering a Symmetrical Snowflake Within Nature, the Nickname of “Pollock” During the 1950’s, the Reason Pollock’s Works Are Similar to Fractals, the Connection Between Fractals and Nature, the Reason Canadian Physicist Richard Edward Taylor Was Able to Replicate Pollock’s Works During the Late 1990’s, the Mathematical Fractals of Trees, the First Person to Replicate Nature Within Artwork, Pollock Discovering the Concept of Fractals Within His Artwork, the Reason Clouds Act as Fractals, the Reason Rocks Act as Fractals, the Complexity of Fractals Predicated Upon Simplistic Rules, the Reason Trees Act as Fractals, the Person Who Discovered Fractals, the Most Well Renowned Work of Polish Mathematician Benoit Mandelbrot, Mandelbrot Hypothesizing That Fractals Control Nature, the Work U.S. Computer Researcher Loren Carpenter Was Blockaded Upon During the 1980’s, Carpenter Attempting to Create the First Computer Generated Imagery of a Mountain, the Reason Carpenter Was Forced to Create an Algorithm for Computer Generated Imagery Animation, the Difficulty of Creating Basic Three Dimensional Shapes Within Computer Generated Imagery During the 1980’s, Carpenter Reading the Work of Mandelbrot, Carpenter Searching for a Method to Utilize Mandelbrot’s Mathematics Within Computer Generated Imagery, the Idea Carpenter Developed to Produce Computer Generated Imagery, Carpenter Leveraging Mathematics to Create Computer Generated Imagery, the Benefit of Applying Fractal Mathematics Toward Computer Generated Imagery, the Traditional Speed of Creating Computer Generated Imagery Animation by Hand vs the Modern Day Speed of Creating Computer Generated Imagery Using Fractals, the Person Who Co-Founded U.S. Animation Studio Pixar, Pixar Leveraging Fractal Mathematics to Create Computer Generated Imagery, and the Various Aspects of the Universe Which Fractals Control