# Alg 1 7 Fractals opening

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```					What Are
Fractals?
Why Study
Fractals
What are the
Mathematics
of fractals
Where are
fractals in
the world?
What is the
history of
fractals?
What is fractal
research
used for?
How are chaos
and fractals
related?
How do you
make a
fractal?
What are we
learning from
fractals?
What are some
famous fractals
and why
are they famous?
Group 1
Step 1   Step 2   Step 3   Step 4   Step 5
Group 2
What are Fractals?
They're everywhere, those bright, weird, beautiful shapes called fractals. But
what are they, really? Fractals are geometric figures, just like rectangles, circles
and squares, but fractals have special properties that those figures do not have.

Geometrical Shapes
Steps to making a fractal

Step 1

Step 2

Step 3            Step 4
How To Make A Fractal

Take a familiar geometric figure (a triangle or line segment,
for example) and operate on it so that the new figure is
more "complicated" in a special way. Then operate on
that figure in the same way and get an even more
complicated figure. Then you do it again and again...and
again. Can you think of it being done an infinite number
of times?
Group 3
Chaos is the study of systems that although appear to
exhibit random behavior, and a fractal is a rough or
fragmented geometric shape.
We should study fractals because the knowledge that
we have is too old, fractals ill make a lot easier to
understand math with our technology from this days.
Fractals are geometric figures, just like
rectangles, circles, but fractals have
special properties. (graphs, functions, and
imaginary numbers.
Group 4
FRACTALS
FRACTALS
BY RAY, MEGAN, AMBER AND CARISSA

BY RAY, MEGAN, AMBER AND
CARISSA
What are Fractals ?
• Fractals are created
by either a
mathematical
iteration process or by
repeating a geometric
process on a
Euclidian form or
• . Fractals can be displayed visually.
Whether for better or for worse, they tend
to be better known for their visual
appearance rather than their mathematical
structure.
• . Fractals are shapes
which are
independent of
scale; no matter how
far you zoom in you
will always observe
the same degree of
'roughness'.
THERE ARE
FRACTALS ALL
OVER THE WORLD.
Group 5
FRACTALS
OUR GALLERY
OF
FRACTALS
BY NIKKI, CATALIN, AND SKYLER
What are fractals?
Fractals are the
repetition of the same
object or alike objects
to make a picture.
What are they used for?
• They are used for
movies, artwork,
math,
computers, Science,
and Engineering.
How are chaos and fractals
related?
• Fractals appear as weird attractors in chaotic systems.
But fractals shouldn't be confused with chaos since they
have different patterns. The words that describe chaos
are dependence and unpredictability. The words that
describe fractals are self-similarity and invariance of
scale.
• One important way Chaos and Fractals are the same is
they are both feedback systems. Feedback systems are
systems where the current outputs will be the inputs of
the next state.
What are some famous fractals and
why are they famous?
• This is the Sierpinski’s
many of it’s triangles.

• This is The Mandelbrot
Set. It is set as a black
cardioid, cardioid means
heart shaped figure.
More famous fractals

• This is the Koch
Snowflake.
Group 6
Fractals
What is a fractal?
A fractal is a complex geometric shape. Any
type of complex shape, shows self similarity
are classified as fractals. They are forms of
simple geography.
Chaos
What is chaos?
What is the difference between
fractals and chaos?
Where can you find fractals and
chaos in the world?
Group 7
FRACTALS

BY
TANNER,CARLI,………………………
…………………………and amy
FRACTALS

What are fractals?
Fractals are geometric shapes which is a self-
similar and has fractional dimensions. They
are anything that contains self image within
its self.
Fractals
• Why study fractals?
• They’re new
• You can understand
them
• Fractals often look
like objects in nature
• People use them to
solve real world
problems
FRACTALS

• What are some famous fractals and why are they famous?
• Fudge flake-because it alternating between different versions
of the modified results in making the fractal non-symmetrical.
Fractals
• another famous fractal.
• Star Fractal-if you check
the total length of all the
stars at the first several
interactions you will find
that the length is
increasing with every
interaction. The sum of
an increasing sequence
of numbers is always
infinite. This means the
Star Fractal is infinite in
length.
FRACTALS
• BY TANNER
• CARLI

• AND amy
Group 8
is fractal?
Whatis aafractal?
What
A fractal is a rough or fragmented
geometric shape that can be
subdivided in parts. The word
fractal comes from the Latin verb
frangere which was derived by
Mandelbrot. A fractal goes on
infinitely.
How do you make a fractal?
shape. Like this.
shape. Like this.
And keep repeating it infinitely.
Like this.
Where are fractals in the world?
Group 9
Fractals

By, Chaseton Ashton,
James Birdsall,
Kassidy Heaps,
Rob King
Question
What is a
fractal?
• A geometrical shape
which is similar and
has fractional
dimension.
• And gives people a
new perspective on
different things.
Question

• How do
you make
a fractal?
• Taking a
picture and
bunch of
different
colors and
designs
Question

•Where
are
fractals
in the
world
• They are
everywhere!
• You can make
one out of
almost
everything
• Like plants
•THE END
Group 10
Fractals

By Jordin, Nichole, Hope, and
Cortney
What is a fractal?
How are fractals and chaos
related?
•   Fractals are graphs of chaotic systems.
Group 11
Fractals
By: Erinn, Elora, Dayna,
Sage, and Heidi
What are Fractals?
 Fractals are rough,     There are many
geometric shapes,        mathematical
subdivided in parts,     structures, such as:
and reduced in size.     Sierpinski triangle,
 Fractals represent       Koch snowflake,
real world objects       Peano curve, and
such as clouds,          Mandelbrot set.
mountains, and          They are generally
turbulence.              similar, and have an
independent scale.
 By: Sage
How do we make fractals?
 A fractal is a design
based on a math
problem. The color is
determined by the
number of iterations it
takes for the point to
leave the coordinates
available on the
graph.
 By: Elora
Why study fractals?
Most math you study in school is old
knowledge. Like geometry you study
about circles, squares, ect. was organized
by a guy named Euclid around 300 BC
However, much of fractal geometry is
much newer. Study of fractals is continued
right now by machinations.
By: Dayna
What’s the history of fractals?
 Fractals started in the late 19th and early
20th century. People explored and made
mathematicians of there date, and
contributions they need to the pre-nascent
field of fractals.
 By: Heidi
Credits
Information gathered from the internet.

Written by Elora, Dayna, Sage, and Heidi.

Persentation created by Erinn.

Laptops and help provided by Ms.
Holdaway.
Group 12
Fractals
Fractals

By Randy and Jared

By Randy Bennett
and Jared Hall
What are
Fractals???
Fractals are basically n
ever ending patterns that
usually use geometric
figures.
What are fractals
used for?
Fractals are used by
engineers to figure out
how to build bridges,
Factories ect.

```
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