FRACTAL

Amgad Hussein, Maria Tokarska, Edward Grinko, Dimitar Atassanov, Megan

Varghese, Emilio Asperti

GEOMETRY

"Clouds are not spheres, mountains are not

cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” – Benoit Mandelbrot

Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have.

They are mathematical hydras that replicate themselves by fragmentation

What is Fractal Geometry?

Fractal patterns come in infinite varieties One property is being very crinkly. Being crinkly

means that very long lines and very large areas have a structure that fits them into very small spaces.

Another essential quality of fractals is self-similarity on very different scales: a small piece of the Dragon has the same general pattern as does a large piece of the dragon.

These two qualities are also commonly found in nature, and there are many references to fractals in nature.

Properties of Fractals

The Human Circulatory System: If all of the veins,

arteries and capillaries in an adult human were laid out end-to-end, then the total length would be over 50,000 miles long! That is lots of crinkliness.

Also, small branches of a tree have the same patterns, same angles and shapes as large branches of the same tree. Sounds like a fractal to us!

Similarly, it is not hard to find a rock with small scale fractures, lines, bumps and patterns that have the same form as the large scale fractures, lines, bumps and patterns on the formation of which the rock is a part. SO fractally!

Fractals in Nature

Architects Fashion Designers Animation people Mathematicians (duh!) Engineers

Fractalian Careers

A mathematical set of points whose boundary

is a distinctive and easily recognizable two dimensional fractal shape

Images of the Mandelbrot set are made by taking numbers on the complex plane, calculating whether it tends to infinity when the formula is iterated on the number, then using the number as X and Y coordinates in the picture and coloring the pixel depending on whether it tends to infinity or not.

Mandelbrot Sets

the set of points which do not approach

infinity after is repeatedly applied consists of values such that an arbitrarily

small modification can cause drastic changes in the sequence of iterated function values.

Julia Sets

We know you saw the movie, but did you read

the book? Did you notice the bizarre drawings on the chapter heading pages? That’s right, those were Jurassic Park Fractals

Now we, as a class, will make the Jurassic park fractal

ENJOY!

Jurassic Park Fractal

http://cs.unm.edu/~joel/PaperFoldingFractal/

paper.html

SIMULATION