*What is a Fractal?
A Geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry.
Fractals are used especially in computer modeling of irregular patterns and structures in nature.
[French from Latinfrctus, past participle of frangere, to break.]
The Sierpinski Triangle- every triangle is divided into four, with the
center being taken out. This keeps going, making it a fractal.
The different steps in making the Koch Snowflake
What are fractals used for?
In our project we learned how to use fractals as a form of image compression. We all made our own fractals by choosing a Julia Set or an, using z as a complex number and c as a constant.
Jenn's Fractal- 0.5 z2-c http://www.wpi.edu/~goulet/jen.JPG
Tony's Fractal- z4+c http://www.wpi.edu/~goulet/tony.JPG
Isabel's Fractal- z3-z2+c http://www.wpi.edu/~goulet/isabel.JPG
Chuck's Fractal- z3+c http://www.wpi.edu/~goulet/chuck.JPG
We also learned how to figure out fractal dimensions using the formula log(parts kept) \ log(total sides)
In the above, Koch Snowflake, the dimension is 1.26
log(4) / log (3)
Other things that involve applying fractals:
Turbulence in Fluids
Complex Number Bases in Computer Science
Surfaces for Heat Transfer
Nerve Regeneration/ Tissue Cells
Grammar School Mathematics
Other Links related to fractals: