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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 1918.
• 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*4/3*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 PageMaker
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 Michael
Crichton put it in his book
“The Jurassic Fractal”.
•The math used for this is iterations.
•Aristid Lindenmayer a biologist from Hungry
developed 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.
• 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.
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.
PRESENTING TO YOU…
Sources
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http://www.math.utah.edu/~alfeld/math/m
andelbrot/mandelbrot.html
http://www.olympus.net/personal/dewey/
mandelbrot.html
http://mathpaint.blogspot.com/2007/03/py
thagoras-tree.html
http://www.2dcurves.com/fractal/fractalp
e.html
http://www.mcgoodwin.net/julia/juliajewel
s.html
http://ejad.best.vwh.net/java/fractals/juras
ic.shtml
http://en.wikipedia.org/wiki/Dragon_curve
http://en.wikipedia.org/wiki/Sierpinski_tri
angle
http://en.wikipedia.org/wiki/Iterated_funct
ion_system
http://mathworld.wolfram.com/StarFractal
.html
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http://www.nahee.com/spanky/www/fracti
nt/juliabrot_type.html
http://homeschoolblogger.com/explorer/7
65735/
http://mathworld.wolfram.com/KochSnow
flake.html
http://www.fractalsciencekit.com/types/or
bital.htm
http://www.bugman123.com/Fractals/inde
x.html
http://www.tnlc.com/eep/circles/
http://www.chaospro.de/bifurcation.php
http://en.wikipedia.org/wiki/L%C3%A9vy_
C_curve
http://en.wikipedia.org/wiki/L-system
http://en.wikipedia.org/wiki/Koch_snowfla
ke
http://dictionary.reference.com/browse/M
andelbrot+set
Sources…part 2
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http://en.wikipedia.org/wiki/Pythagoras_tr
ee
http://en.wikipedia.org/wiki/Peano_curve
http://en.wikipedia.org/wiki/Julia_Sets
http://hubpages.com/hub/Defining-theFractal
http://www.fractalsciencekit.com/types/or
bital.htm
http://en.wikipedia.org/wiki/Dragon_curve
http://en.wikipedia.org/wiki/Circles_of_Ap
ollonius
http://www.nahee.com/spanky/www/fracti
nt/juliabrot_type.html
http://en.wikipedia.org/wiki/L-system
http://en.wikipedia.org/wiki/Iterated_funct
ion_system
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http://en.wikipedia.org/wiki/L%C3%A9vy_
C_curve
http://en.wikipedia.org/wiki/Sierpinski's_T
riangle
http://en.wikipedia.org/wiki/Bifurcation_fr
actal
http://egregores.blogspot.com/2010/12/ex
tremely-cool-natural-fractals.html
http://en.wikipedia.org/wiki/Iteration
http://en.wikipedia.org/wiki/Formula
http://www.merriamwebster.com/dictionary/y-intercept
http://dictionary.reference.com/browse/s
egment
http://www.funnyphotos.net.au/fractal/
http://www.ultrafractal.com/