Fractals

1
Fractals

• A lesson for 3rd grade
• Rose Horan

Click on me! Cali the alligator!
2
Where do you want to go?

• History of Fractals
• Definition of fractals
• Examples
• Fractal or Not Game?
• NCTM Standards
• Fractals Everywhere
• Fractal Food
• Virtual Manipulative
• References

Click on the pink arrows!!
3
History of fractals

• The word fractal did not exist until 1975
• Benoit Mandelbrot is considered to be the
  fractal father of geometry

4
History of Fractals cont

• Mandelbrot needed a name for his shapes,
  dimensions and geometry.
• Mandelbrots son was home from school.
• Mandelbrot was going through his sons Latin
  Dictionary. He came across the adjective
  fractus, from the verb frangere, to break. The
  resonance of the main English cognates fracture
  and fraction seemed appropriate. Mandelbrot
  created the word (noun and adjective, English and
  French) fractal.

5
Definition of Fractals

• Rough or fragmented geometric shapes that can be
  subdivided in parts, each of which is a reduced
  size of the whole
• Any pattern that reveals greater complexity as it
  is enlarged
• Closer you come the more detail you see
• Repeating pattern
• Self similar
• World within worlds

6
Examples
A coast line is good example. The closer you get
to the coastline, the more detail you see. The
area also increases.
This pattern is repeating. There is a world
within worlds.
7
Fractal or Not?

• Which items are fractals? Click on them

8
NCTM Standards

• Recognize geometric shapes and structures in the
  environment and specify their location.
• Create mental images of geometric shapes using
  spatial memory and spatial visualization.
• Recognize, name, build, draw, compare and sort 2
  and 3 dimensional shapes.

9
All of these items have fractals on them
Greeting Cards
Coffee Mugs
Clothing
Pictures
Jewelry
Notebooks
10
More items that have fractals.
Magnets
Clocks
Mouse Pads
Tile Boxes
Stickers
Ornaments
Posters
Tote Bags
11
Examples found in nature
Snowflakes
Shells
Tree Branches
Ferns
Clouds
Cloud Nebula
12
More Nature Examples
River systems
Stalagmites
Lightning
Mountain Ranges
Leaf Veins
13
Close up view of a fractal
The closer you come to the object the more detail
you see.
14
Close up view of fractal food
Broccoli
The closer you come to the object the more detail
you see.
15
Definition of Fractals

• Rough or fragmented geometric shapes that can be
  subdivided in parts, each of which is a reduced
  size of the whole
• Any pattern that reveals greater complexity as it
  is enlarged
• Closer you come the more detail you see
• Repeating pattern
• Self similar
• World within worlds

Click on the question mark to go back to the game
16
TRY AGAIN!!YOU CAN DO IT!!!
Click on the dog if you need extra help.
Click on Sun to go back.
17
TRY AGAIN!!YOU CAN DO IT!!!
Click on the dog if you need extra help.
Click on Sun to go back.
18
TRY AGAIN!!YOU CAN DO IT!!!
Click on the dog if you need extra help.
Click on Sun to go back.
19
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
20
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
21
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
22
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
23
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
24
CORRECT!!!AWESOME JOB!!
Click on the girl to go back.
25
For more practice Try Virtual Manipulative

• http//nlvm.usu.edu/en/nav/frames_asid_136_g_2_t_3
  .html?openinstructions
• http//nlvm.usu.edu/en/nav/frames_asid_135_g_2_t_3
  .html?openinstructions
• http//nlvm.usu.edu/en/nav/frames_asid_137_g_2_t_3
  .html?openinstructions
• Click on the links above and check out the
  websites! Write two (2) paragraphs about what
  you learned and how fractals are in everyday life.

Click on Cali!
26
References
Click on Cali!

• http//standards.nctm.org/document/chapter4/numb.
  htm
• http//growabrain.typepad.com/growabrain/2004/09/g
  rowabrain_frac.html
• http//www.west.asu.edu/achristie/548/02WQ/linda/F
  ractals_files/image004.gif
• http//www.allegria.com.au/Prod_Fractals.html
• http//www.dcrimages.com/cgi-bin/store/fractal.cgi
  /ovalstickers/dcrimages.16563370
• http//mathworld.wolfram.com/Fractal.html
• http//www.cafepress.com/spiritkeep01.8500187
• http//www.dcrimages.com/cgi-bin/store/fractal.cgi
  /clocks/dcrimages.16534955
• http//www.dcrimages.com/cgi-bin/store/fractal.cgi
  /mousepads/dcrimages.16427367
• http//www.healingdaily.com/detoxification-diet/br
  occoli.jpg
• http//www.ybdigitals.com/images/Resize20of20Wid
  e20clouds20D204-1Hz.jpg
• http//www.sciencemuseum.org.uk/antenna/motherland
  /images/tree.jpg
• http//nlvm.usu.edu/en/applets/controller/query/qu
  ery.htm?qtfractals
• http//images.google.com/imgres?imgurlhttp//clas
  ses.yale.edu/fractals/Panorama/Nature/NatFracGalle
  ry/Gallery/LightningS.gifimgrefurlhttp//classes
  .yale.edu/fractals/Panorama/Nature/NatFracGallery/
  Gallery/Gallery.htmlh100w100sz10tbnid8TDlu
  7zefFgJtbnh77tbnw77hlenstart78prev/imag
  es3Fq3Dfractal2Blightning2B26start3D6026svn
  um3D1026hl3Den26lr3D26sa3DN
• http//www.bucka-lassen.dk/flacroz/pictures/0604_5
  _Nullarbor_coast_line.jpg
• http//images.google.com/imgres?imgurlhttp//www.
  byers.us.fm/Fractals/Animations/300/design857.gif
  imgrefurlhttp//www.byers.us.fm/Fractals/Animatio
  ns/Headers/Tubes.htmh225w300sz379tbnidx_Sc
  R8WaKSwJtbnh83tbnw111hlenstart17prev/im
  ages3Fq3Dcartoons2Bdancing26svnum3D1026hl3D
  en26lr3D