**Fractals Research Projects**

How would you describe what a fractal is to your parents/guardians?

I will say that a fractal is a never ending pattern that repeats itself with the same designs over and over.

What are some properties that are true of all fractals?

Two of the most important properties of fractals are self-similarity and non-integer dimension.

Introduction

A fractal is a geometric pattern that is repeated at ever smaller (or larger) 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 found in nature.

What are the different types of fractals and where are they found in nature?

The types of fractals are The Koch Snowflake,the Jurassic Park fractal,Julia sets,Mandelbrot sets and Star fractals.

They can be found in Mountains,

Rivers, in a leaf, clouds,snowflake, lightening, peacock and crystals or ice.

What are some famous fractals that have been created?

The "self-similar" nature of fractals means that particular elements, such as the Mandelbrot set, reappear over and over again, no matter how "deep" one goes into the image through magnification.

Are fractals used for any practical purposes? Why are people

interested in

fractals?

What do you find interesting about fractals?

I found interestion about fractals are it's different uses in many things like in a computer or it's designs in nature like the lines of leaf.

Introduction 2.

Relative to this art form, fractals are a unique, digital art form, using mathematical formulas to create art with an infinite diversity of form, detail, color and light. In simple terms, a fractal is a graphical representation of a mathematical equation. The formula used for a particular image determines how each pixel in the image is formed and colored. A typical fractal image contains millions of these pixels.

These complex images of extraordinary beauty can arise out of fairly simple mathematical formulas, and then by selectively modifying these formulas, changing coloring algorithms etc. one can create unique compositions previously unseen to the human eye.

In this detail of the Mandelbrot set, the set itself appears in black, with the fractal boundary alive with color.

Yes the fractals have different purposes in astronomy for example fractals will maybe revolutionize the way that the universe is seen. Cosmologists usually assume that matter is spread uniformly across space. But observation shows that this is not true. Astronomers agree with that assumption on "small" scales, but most of them think that the universe is smooth at very large scales. We also use them in computer science, actually, the most useful use of fractals in computer science is the fractal image compression. This kind of compression uses the fact that the real world is well described by fractal geometry. That's whay people is interested in fractals because of it's different uses and designs.