Iteration

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A mathematical expression like z←z*z+c is to be interpreted as follows:

follow the instructions to the right of the ← and replace the number to the left of the ← with the result, repeating until some specified condition is met.

Each replacement with the results of the calculation to the right of the ← is called an iteration. The condition to be met to halt the iterations may be a specified number of iterations or may be reaching some limit based on the calculated result. The maximum number of iterations allowed is called the depth, d, of the iteration operation.

The iteration operation sort of lets a mathematical system have its head and take you where it naturally wants to go.