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Category Archives: Fractals
The Collatz Fractal
In the past, we have spent a significant amount of time discussing the Mandelbrot set and variations thereon. We saw that each Mandelbrot, multibrot, and Julia set can be characterized as a set of complex numbers that behave “nicely” with … Continue reading
The Mandelbrot Set—Part VII: Multibrot Sets
The Mandelbrot Set Series: This is the seventh part in a series on Mandelbrot set fractals. In the previous post, we varied the constant term in the Mandelbrot set generating function, which gave us an infinite variety of Julia sets. … Continue reading
The Mandelbrot Set—Part VI: Julia Sets
The Mandelbrot Set Series: This is the sixth part in a series on Mandelbrot set fractals. Up until now, we have looked at fractals that are generated by examining the limit behaviour of points on the complex plane when a … Continue reading
The Mandelbrot Set—Part V: Coloring the Mandelbrot Set
The Mandelbrot Set Series: This post is the fifth in a series on the Mandelbrot set. Thus far, we have managed to define the Mandelbrot set as a collection of points or numbers on the complex plane. Every point is … Continue reading
The Mandelbrot Set—Part IV: Defining the Mandelbrot Set
The Mandelbrot Set Series: This post is the fourth in a series on the Mandelbrot set. In previous posts, we have discussed what fractals are, given a hint as to the complexity of the Mandelbrot set, and laid some groundwork … Continue reading
The Mandelbrot Set—Part III: Complex Numbers
The Mandelbrot Set Series: This post is the third in a series on the Mandelbrot set. The Mandelbrot set resides upon the complex plane. This means that in order to look more closely at the Mandelbrot set itself, we need … Continue reading
The Mandelbrot Set—Part II: Exploring the Mandelbrot Set
The Mandelbrot Set Series: This post is the second in a series on the Mandelbrot set. In this post, we are going to spend some time exploring the set, in order to get a feel for some of the structures … Continue reading
The Mandelbrot Set—Part I: Fractals
Every Monday for the past several weeks, I have posted an image under the heading Monday Mandelbrot Madness. I have offered up these images largely on aesthetic grounds, and offered very little in the way of mathematical explanation. There are … Continue reading