![]() ![]() It was awesome to see the bulbs emerge but I soon realised that I couldn’t zoom in as much as in the video. I think this was one of the first things I tried to program. If we count how many iterations it takes for points to leave a circle of radius 2 (beyond this value it is impossible to avoid going to infinity) then we can use this to colour the points close to the boundary, this is what the rich colours in the visualisations in this article mean.Īs a teenager I was inspired and tried to make my own zoom in java. ![]() The points where the value does not tend to infinity are considered inside the Mandelbrot set. Symbolically, \(z = z^2 + c\) where \(c\) is our number and the initial value for \(z\) is \(0\). It says that if I start with \(0\) then add this number, then square the result and add this number again and square and add repeatedly, does the value blow up? For example, in the main bulb a constant value is tended to whereas in the secondary bulb the output of the algorithm settles down to ping back and forth between two values. The number in the bulb is the number of points in the limit cycle the points in that area tend to. Fig: The Mandelbrot set with the real and imaginary axis shown. Surprisingly, the formula to generate the image can be written in just a few lines of code and if you know what a complex number is, is very easy to understand.īefore any zooming takes place the image we are looking at is displaying the output of an algorithm applied to a range of complex numbers with real parts from -2 to 1 and imaginary part from -1 to 1, as shown in the figure below. The structure that is being zoomed into above is called the Mandelbrot set. I thought that there must be some complicated mathematics that was being used to generate the image but I couldn’t imagine what it could be. ![]() Have you ever watched one of those super deep fractal zoom videos? I saw this one in particular back in high school and remember being blown away how was such beauty being constructed? ![]()
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