Fractals Project

1. Fractals Project Linda Rubio

2. Some Fractal Types • Peano Curves • Star Fractal • Sierpinski’s Triangle • Pascal’s Triangle • The Lorenz Fractal • The Mandelbrot Set • Polya’s Sweep • The Levy Curve • The Cesaro’s Sweep • Snowflake Fractals • The Dragon Fractal • “Ifs”Fractal (Iterated Function System • Julia Fractal • The Pythagoras Tree • Plasma Fractal • Lambda Fractal • Julibrot Fractal • Newton Fractal • The Symmetric Icon • The Circle Fractal

3. What are Fractals? It is a geometric pattern that is repeated at ever smaller scales to produce irregular shapes. Fractals are used especially in computer modeling of irregular patterns and structures in nature. Clouds are in a form of nature that we see everyday.

4. What is a complex number? A complex number is like an imaginary number. When we don’t know the letter’s value we have an imaginary number like 1 to substitute the letters value.

5. Mandelbrot • This fractal was first explain by a French mathematician by the name of Benoît Madelbrot. • The Mandelbrot set is made up by complex numbers. Set http://www.youtube.com/watch?v=G_GBwuYuOOs

6. Peano Curve This fractal was first examined and explained by Guiseppe Peano. It was named after him. ”Peano Curve” Means a curve passing through every point of a two dimensional region. This means that a peano curve is not just a curve, but a curve that became so twisted that became 2 dimensional. http://www.youtube.com/watch?v=4RQmLNa5ZNo My favorite Fractal because of the way it looks*

7. Pascal’s Triangle Pascal’s Triangle was named after Blaise Pascal. They say that this fractal was discovered by the ancient Chinese.

8. Plasma Fractal • They are known as a “noisy image”. • They are the most common type of fractals. We see them everywhere. Clouds are a plasma fractal. • The movies that we watch in special effects contain a lot of this fractal. They divide the image into squares and pick where in the square the “noisy image” will fade and start fading. To me it is a very hard fractal since they form it on the computer.

9. Dragon Fractal This fractal is a member of a family of self similar fractal curves. It is formed with 90〫angle. The math used in the fractal is trigonometry. http://www.youtube.com/watch?v=BdaOwIHK5cc

10. Repetition Repetition means to do something over and over (repeating). Fractals are all about repetition. They are so beautiful because they have small patterns in a bigger pattern and so on.

11. Infinite Infinite means that there is no end. Pattern A pattern is almost a repetitive shape but it could change. A fractal is beautiful because of the strange patterns.

12. I really found it hard to search for this project of fractals. They are very hard to explain. The math used in the fractals are math I don’t even understand. It was hard to find out anything on certain fractals. Some didn’t really have much information. Do we know all fractal types? One day I want to create my own official fractal. I want to be able to explain it knowing everything about it. Talking to the people who are doing the fractals project too made me think outside the box. What if our planet is fractal. What if we are small patterns in a humongous world? I really started to think about it. My thoughts, Ideas and conclusions on Fractals