Fascinating Fractals!
Investigate fractals with me — amazing iterated patterns with zoom similarity! I discuss many examples of fractals, including the Koch snowflake enclosing a finite area but with an infinite perimeter and the Sierpinski Triangle, which has no area at all! In addition, the Sierpinski Triangle is of dimension 1.58, reflecting its position in the nether world between dimension 1 and 2!
Find out how Fractals are found in art, medicine, science, technology, and more!
Yep, Fractals seem weird but abound indeed!
My Fractal Chaos Activity!
Is There Order out of Chaos?
After doing this hands-on activity you should see a familiar pattern! I have often presented it in my workshops on Fractals, and it was always a huge “forehead knocker”! (a.k.a., a huge hit!)
Materials:
Clear transparent paper (one per person)
Markers or pens: red, blue, green (one of each color per person)
Regular 6-sided dice (one per person)
Pre- Assembly:
For each person: Print or draw the same size large equilateral triangle (~ 6 inches per side) on a transparent sheet.
Activity:
Pass out the transparent sheets, one to each person:
Each person receives 3 pens (one each of red, blue, and green) and one die
Have each person mark a dot any place on or inside the interior of the triangle with any one of the pens. This is the “starting point”
A new starting point will be found by each roll of the die....
o If the roll is a 1 or a 2, select the red pen and mark a red vertex.
o If the roll is a 3 or 4, select the green pen and mark a green vertex.
o If the roll is a 5 or 6, select the blue pen and mark a blue vertex.
After each roll of the die, mark with the proper colored pen a new dot midway between the last starting point and the same pen-colored vertex.
Each person repeats rolling a die and marking dots 30 or more times.
After each person has finished, have them lay their transparency over the others, lining up the correct colored vertices (helps to layer sheets on a light table source)…. Ask: What do you notice? A very familiar pattern will appear! Enjoy!