Diagram of loop

The "initial condition" in this case is a point on the map (called C) which we are testing to see if it lies inside the Mandelbrot Set. The actual test is shown in the next diagram.

The "input condition" in this case is also a point on the map (called Z). When we start off, this is the same point as C.

What I have called "Mandelbrot's Jump" (probably nobody else calls it that) is the set of rules for jumping to a new location on the map - for producing a new Z, in fact. Notice how this is similar so far to what happens when we create a new generation in Conway's Game of Life.

We'll be looking at those rules in the diagram after the next one. The actual transformation is simple: the new position = Z2 + C. This becomes the new Z, which is fed back into the loop.

We can look at that formula until our eyes water, and it doesn't really tell us anything. The real significance of it should become clear over the next two diagrams (I hope!). For now I will just mention that squaring a complex number, as in Z2, may not do what you think it does!

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