Fractals & Chaos Assignment for 9/13

As promised, here is the video I mentioned in class discussing further categories of infinity. I also recommend this Numberphile video to further clarify the difference between the two infinities we talked about in class (countable vs. uncountable)

We created a Koch Snowflake in class today and talked about some of the mathematical implications of its borders. Tonight, please finish drawing the image of the Sierpinski Triangle using the dot sheet you got in class:

  1. Draw a triangle connecting the three dots marked
  2. Find the midpoints of those three sides and connect them, creating four congruent triangles.
  3. Shade in the middle triangle (the one pointing down). This “removes” that triangle from the image and the remaining three represent Iteration 1 of the Sierpinski Triangle process.
  4. For all triangles that remain, connect the three sides and shade in the middle triangle formed.
  5. Continue this process as small as the scale will permit.

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