The Koch Snowflake

Fractals are a never ending pattern

They are created by repeating a process

There are different processes for each of the different types of Fractals.

Saturns rings

Images were sent form a NASA mission showing that Satrurns rings were Cantor-like sets. There was no convincing fractal analysis, however after looking at the pictures taken they used the threebox-counting method and found the demnsions of the edges of the rings were consistantly about 1.63-1.78 This showed that it is a Fractal

**Fractals in Astronomy**

**Contents**

What are Fractals?

Examples of Fractals

Mandelbrot Set

Cantor Set

Three box counting method

Saturn's Rings

Galaxies

Variable Stars

Fractals

MandelBrot Set

GALAXIES

The Sierpinski Gasket

Cantor Set

Pulsating Stars

Barile, Margherita and Weisstein, Eric W. "Cantor Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CantorSet.html

"Fractal." Wikipedia. Wikimedia Foundation. Web. 31 May 2015.

"Fractal Cosmology." Wikipedia. Wikimedia Foundation. Web. 31 May 2015

Gardi, L. "The Mandelbrot Set and the Fractal Nature of Light, the Universe, and Everything." 2013. Web. 31 May 2015.

Kent, Brian. "Fractals and Astronomy." Dr. Web. 31 May 2015.

Ra, Amateo. "Scientists Find Fractal Patterns & Golden Ratio Pulses in Stars." Spirit Science and Metaphysics. 11 Feb. 2015. Web. 31 May 2015.

Saturn's A Ring From the Inside Out. Digital image. Http://saturn.jpl.nasa.gov/. 9 July 2009. Web.

"Scientists Find Fractal Patterns in Variable Stars." Breaking Science News SciNewscom. 9 Feb. 2015. Web. 31 May 2015.

"What Are Fractals?" FractalFoundationorg RSS. Web. 31 May 2015.

Yirka, Bob. "Researchers Find Evidence of Fractal Behavior in Pulsating Stars." Researchers Find Evidence of Fractal Behavior in Pulsating Stars. 4 Feb. 2015. Web. 31 May 2015.

The Cantor Set is also known as Cantor comb or

No middle third set

This is where the seed is a line and the middle third of the line is taken out, then the process is repeated creating the Cantor Set.

A group of researches in the university of Hawaii, have discovered that the pulses of the RR Lyare stars aren't random but actually pulsate with a golden mean. Astronmers now call these 'Golden' RR lyare stars.

Further research showed that it behaves in a fractal pattern.

Works Cited

Mandelbrot Set of complex numbers that creat a fractal pattern when plotted

Z being the seed

The equation to creat the fractal pattern is

Galaxy distribution in the universe was said to not be unifromily distributed, they were thought to be random. Mandelbrot analyzed this and found that to a certain point galaxies were fractaly distributed.

Made by a recursive process

Starts with the seed, which is an equilateral triangle

Then add an equilateral triangle a third of the size of the seed, to each of the seeds sides.

The Sierpinski Gasket is also made by a recursive process

You start with a seed triangle and remove the triangle that is connected to the midpoints of each other seeds side.

Barile, Margherita and Weisstein, Eric W. "Cantor Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CantorSet.html

"Fractal." Wikipedia. Wikimedia Foundation. Web. 31 May 2015.

"Fractal Cosmology." Wikipedia. Wikimedia Foundation. Web. 31 May 2015

Gardi, L. "The Mandelbrot Set and the Fractal Nature of Light, the Universe, and Everything." 2013. Web. 31 May 2015.

Kent, Brian. "Fractals and Astronomy." Dr. Web. 31 May 2015.

Ra, Amateo. "Scientists Find Fractal Patterns & Golden Ratio Pulses in Stars." Spirit Science and Metaphysics. 11 Feb. 2015. Web. 31 May 2015.

Saturn's A Ring From the Inside Out. Digital image. Http://saturn.jpl.nasa.gov/. 9 July 2009. Web.

"Scientists Find Fractal Patterns in Variable Stars." Breaking Science News SciNewscom. 9 Feb. 2015. Web. 31 May 2015.

"What Are Fractals?" FractalFoundationorg RSS. Web. 31 May 2015.

Yirka, Bob. "Researchers Find Evidence of Fractal Behavior in Pulsating Stars." Researchers Find Evidence of Fractal Behavior in Pulsating Stars. 4 Feb. 2015. Web. 31 May 2015.

Works Cited

Three box counting method

Is also known as Grid method.

It is used to calculate the fractal dimensions in complex objects.

You start by covering an area with squares and repeating this but with different sized squares. Then calculate the ratio of grid sizes to the number of grids containing the objects.

To calculate objects with volume we use boxes instead of grids.

The equation to calculate the ratio is