As per Wikipedia: The Mandelbrot set is the set of complex numbers c for which the function f_c(z) = z² + c does not diverge when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc, remains bounded in absolute value.

f_n+1(z) = z_n² + c
f₀(z) = c , when z = 0
f₁(z) = c² + c
Let c = a + bi
c² = (a + bi)(a + bi)
     = a² - b² + 2abi

Based on the above formula, check for all of the possible values and see if it goes towards infinity or stays bounded.

Here the canvas is a 2D plane, which can represent a complex number a + bi across the x and y axes.

While the formal definition of Julia Set is there, in this context, I want to point out that Julia Set is deeply connected to the Mandelbrot Set.

A quick way to describe the relation is that the c in the formula of Mandelbrot Set which we keep updating from the previous iteration:

f_n+1(z) = z_n² + c

is just a constant (complex number) for Julia Set.