Let's say we have a point on an XY coordinate plane: $A(0.2, -0.1)$ We need to find if it's located in the mandelbrot set using the equation $z'=z²+c$ which means turning point A into a complex number.

I'm having trouble understanding the complicated symbols Wikipedia provides so I need help with turning points into complex numbers and using them in the equation.

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Your point is $$A=\left(\frac{1}{5},-\frac{1}{10}\right).$$ We can express it as $a+ib$: $$A=\frac{1}{10}\left(2-i\right).$$ Define the function $$f(z):=z^2+A.$$ Your point will belong to the Mandelbrot set if the sequence $$f(0),f(f(0)),f(f(f(0))),\ldots$$ remains bounded.

This will be the case since $|A|=\sqrt{5}/10<2$ and the disk centered at $0$ with radius $2$ belongs to the Mandelbrot set.

  • $\begingroup$ Thanks but I don't know how to subtract or do anything with i. Sorry maybe I should have put that in my question. $\endgroup$ 2 days ago
  • $\begingroup$ In this case, you should read an intructory book to complex analysis before studying the Mandelbrot set. I recommend the book Visual Complex Analysis. $\endgroup$ 2 days ago
  • $\begingroup$ Also question. When we express it as a+ib why put a 2-i there. Does the two have anything to do with the 1/5? I would expect it to look like 1/5 + -1/10(i). Can you please explain? $\endgroup$ 2 days ago
  • $\begingroup$ I just factored the $1/10$. $\endgroup$ 2 days ago
  • $\begingroup$ Okay thanks. I'll take a look at the book you told me about. $\endgroup$ 2 days ago

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