FRACTALS Math in Nature and Arts

ACTIVITY

Form groups of 2-3 members

Each group will try to draw the picture that fits the sequence of images.

EXAMPLE

ANSWER

ITEM 1

ANSWER

ITEM 2

ANSWER

ITEM 3

ANSWER

THINGS TO THINK ABOUT

What is common among the three items?

Have you seen such patterns in other places? (nature, art, etc)

GUESS WHAT IS IT? By: Alfredo Matacotta

FRACTALS

Applying the operation of shrinking and moving applied many times

Involve symmetry of magnification (called dilation)

it is a shape that you could zoom in on a part of it an infinite number of times and it would still look the same

Coined in 1980 by the Belgian Mathematician Benoit Mandelbrot

FRACTALS EVERYWHERE

FRACTALS IN NATURE

FRACTALS IN NATURE

FRACTALS IN NATURE

FRACTALS IN THE HUMAN BODY

FRACTALS IN ARCHITECTURE

FRACTALS IN ART

EXAMPLES OF GEOMETRIC FRACTALS

KOCH SNOWFLAKE

SIERPINSKI TRIANGLE

https://commons.wikimedia.org/wiki/File:Rep-tile_triangle_creating_Sierpinski_carpet.gif

EXAMPLES OF ALGEBRAIC FRACTALS

MANDELBROT SET

http://functionspace.com/topic/1638/Mathematics-using-gifs-

MANDELBROT SET (MORE VERSIONS)

https://www.tumblr.com/search/mandelbrot%20gif

JULIA SET

http://quantumwavepublishing.com/a-few-fractals/

FRACTAL PROPERTIES

FRACTAL PROPERTIES

Self-similarityappear the same under magnification

Fractional dimensionare not limited to integer dimensions, it can have fractional dimension (e.g. 1.58 or 2.40)

Formation by iterationform by a repeating process

𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑓𝑟𝑎𝑐𝑡𝑎𝑙 𝑠𝑒𝑡 =log(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑒𝑐𝑒𝑠)

log(𝑚𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟)

MAKING FRACTALS

CONSTRUCTING FRACTALS

CONSTRUCTING FRACTALS

CONSTRUCTING FRACTALS

CONSTRUCTING FRACTALS

EXERCISES

EXERCISE: CONSTRUCT THE DRAGON CURVE

LABORATORY

LABORATORY WORK

https://www.wolframalpha.com/examples/Fractals.html