Mandelbrot Set

Fractal pattern

Math

Sqrt(-1) is an imaginary number i
Complex number has a real component (a) and an imaginary component (b): a+bi
Set of complex mapped on canvas with x axis mapping a and the y axis mapping b
Function f(z) = z^2 + c = z^2 + (a + bi)
f(z_0) = 0
f(z_1) = 0^2 + (a + bi) = a + bi = c
f(z_2) = c^2 + c --> need to find out c^2
c^2 = (a + bi) * (a + bi) = a^2 + 2abi + b^2*i^2 = a^2 + 2abi - b^2 = (a^2-b^2) + 2ab * i
--> meaning c^2 is a complex number with a real component a^2-b^2 and and imaginary component 2ab
when calculation iteration over many iterations does result of function stay bounded or goes to infinity