Fractal Project Jessika Evans What exactly is a

Fractal Project Jessika Evans

What exactly is a Fractal? A fractal is produced by complicated numbers that make a complex fractal map. A fractal has many forms and many different equations and shapes. They have extravagant colors that form their patterns while others don’t use color to create their pattern. These forms can be seen naturally in the world around us.

• The repeated pattern is swirls that turn in to circular pattern and it keeps getting smaller. • The colors represent the outer circles, the colors changes the smaller it gets. • The math used is trigonometry. • This fractal was named after Benoit Mandelbrot for he had created it.

You use a two-dimensional unit square to make the fractal. You use iteration math to make the fractal. An Italian logician Giuseppe Peano Constructed the Peano Curve in 1880.

• The math used a two to three dimensional set to make this fractal; the math that is needed is geometry. • The Julia Sets were named after Gaston Julia. • Who is the French mathematician who discovered the fractal which was published in

• The shape that is repeated is originally a star fractal but repeated until it makes a snowflake form. • This fractal uses a complicated formula using Geometry. • This fractal was also know as the Koch island, in 1904 it was first described by Helge von Koch.

• The shape that repeats is a star shape. • The math formula is 3*4/3*4/3*4 infinity. The math used is Geometry. • This fractal is very similar to the snowflake fractal and was created by the same person Helge von Koch but was slightly altered.

• The colors show the repeats in the fractal and how many times it repeats in the fractal. • The math formula to make a orbital fractal is a very complex one it has a 10 step system. • The math type used is algebra. • This was made based on the Mandelbrot sets but was altered in a circular form.

• The formula to create it is extremely complicated. • The math needed to make this fractal is Algebra. • Mark Peterson developed the mechanism for the Julibrot Fractal.

• It uses y-intercept to create itself. • The math it uses algebra. • The circle fractal is based off the yinyang symbol. • It was originally created in the adobe Page. Maker and then later redone in adobe Photoshop.

• This uses simple algebra. • It was first published by Chandler Davis and Donald Knuth. • The dragon fractal got its nickname Jurassic Fractal because author

• The math used for this is iterations. • Aristid Lindenmayer a biologist from Hungry develope and introduced the L-System fractal. • He discovered it from plants and algae.

• The IFS Fractal known as the Iterated Function system can be generated into a number of different functions for example Sierpinski triangle. • The person who discovered it was John E. Hutchinson.

y v Le e v r u C • The math used to figure out the fractal is two segments that form a 90 degree angle. • The math used was geometry. • The properties of the Levy curve were analyzed by Ernesto Cesaro. • But the first person to find the self-similarities of the fractal was a French mathtician by the name of Paul Pierre Levy.

• This fractal uses Iteration as well as many other fractals. • The sierpinski’s triangle was named Waclaw Sierpinski. • This fractal is often made into carpets, this is where it got its nickname Sierpinski’s carpet. s ’ i k s n i p r Sie e l g n Tria

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Common terms used in fractals • Iteration- the act of repeating a process usually with the aim of approaching a desired goal or target or result • Formula- entity constructed using the symbols and formation rules of a given logical language • Y-intercept- the y-coordinate of a point where a line, curve, or surface intersects the y-axis • Segment- one of the parts into which something naturally separates or is divided

Fractal in nature • The L-system is one of the most obvious fractals in nature. • Peacocks feathers are also a form of a natural fractal for how their patterns in their feathers repeat. • Lightening if you look at photos of it has a pattern that get smaller and smaller until you can no longer see.

! ! ! 5 PRESENTING TO YOU… l a t c a r F a r t l U

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