![]() ![]() I hope you get the idea by now and I don't know how close the analogy really is. Then if you choose half a turn, so pi*R which is -1, it alternates between -1 and 1, left and right., just like in this video. It has minimal polynomial This quadratic polynomial has two roots, and The golden ratio is also closely related to the polynomial which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number. ![]() ![]() or right, right, right., like in this video. The golden ratio is also an algebraic number and even an algebraic integer. Starting to the right of what is essentially a trigonometric cirlce (so 1) but that you draw as a X, it gives you 1, 1, 1. Since what you did there in the mandelbrot video is basically taking a C (which is a fraction) within this circle and squaring it iteratively in the 2D plane, this is exactly the same thing the imaginary flower of the example is doing: choosing a fraction of a turn (a C) and square it iterativelly, which is equal to doing the same fraction of a turn over and over because we are in the 2D plane and multiplying two complex numbers is like turning and stretching until their points met. In Ben's mandelbrot video, we see paterns like that forms when you move the value of the constant C within the "non exploding area", between -1, 1, i and -i.īecause of that radius 1 centered on 0, this means this circle contains all complex numbers containing only rational parts. I just saw the other video Ben Sparks did on the mandelbrot set and watching both of them made me realize something about complex numbers.ģBlue1Brown once explained and showed multiplying a number by another on the complex plane was like turnning and stretching a transparant of this plane such as to make the point of the first number correspond to the resulting point/number. ![]()
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