The past few lessons we have been looking at fractals in a very geometric way, creating beautiful and crazy structures. However, today we looked at fractals algebraically. We took a simple function and through iteration were able to create dynamic sequences both bounded and unbounded. What truly amazed me was when we were able to see these points plotted onto a Cartesian Plane and how they created, wild, infinite and incredibly complex patterns and shapes.
We also explored imaginary numbers and how they created bounded sequences. I had previously heard of imaginary numbers and was interested when we were able to apply them to create sequences. The highlight for today’s lesson for me, was being able to visually observe how the imaginary numbers, plotted along with real numbers, moved across a Cartesian plane. I was very interested by this concept and hope to explore further mathematics with imaginary numbers.
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