Wishing you roses red & violets blue…

]]>1. Choose a constant number. Let’s call it C.

2. Take another number – start with the number zero. Let’s call it Z.

3. Multiply the number Z by itself, and add the specified constant C.

4. Repeat Step 3 until Z is bigger than two.

It’s a very simple sequence. Now, obviously, if C is big, then there will be few if any repetitions. If C is very small, then there will be lots of repetitions. Where it gets interesting is if you let C be a complex number with real and imaginary parts – represented in the image by horizontal and vertical respectively, with zero somewhere in the middle of that largest black region – then sometime the repetitions go on forever. And that black figure represents all the values of C for which that happens.

On a personal level: I have all my life (well, from mid-teens, I guess) had a passion for programming computers, and whenever I have learned a new language or a new operating system I have set myself the challenge of learning how to create the graphical image of the Mandelbrot set.

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