Fractals

Similarity, Geometric Series and Measuring some famous fractals

Videos:

Similarity and Area
The infinite geometric series formula
Introduction to Fractals
Calculating length and area for a Sierpinski triangle
Another way you could calculate total length for a Sierpinski triangle (this is probably helpful for the homework)

.pdf of the Sierpinski calculations

Homework Assignment as a .pdf or a .docx(write or type and upload to Canvas)

Fractional dimension

Videos:

TED talk by Benoit Mandelbrot (who first coined the word "fractal")
A discussion of fractal dimension: "fractals are not typically self-similar" by 3Blue1Brown
Calculating the fractal dimension for fractals that are strictly self similar (self similarity dimension) part 1 and part 2

Homework Assignment as a .pdf or a .docx

Fractals from complex numbers: Julia and Mandelbrot Sets

First: watch the video: The Geometry of Complex Numbers

Next: go to How to Make a Fractal and answer these questions available as .pdf or .docx to turn in (First Julia/Mandelbrot assignment) (do your best to answer the questions by observing and interacting with the "how to make a fractal" program, but you can hold onto the assignment and make changes as you watch the next videos too)

Videos:

Recursion and Julia sets (you can also play with the Geogebra sketch )
Julia sets and Mandelbrot sets (the notes from the end of the video) (the cool Mandelbrot/Julia web site)

Second Julia/Mandelbrot assignment .pdf or .docx