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 3.11 Bailout Test

  The bailout test is used to determine if we should stop iterating before
  the maximum iteration count is reached.  This test compares the value
  determined by the test to the "bailout" value set via the <Z> screen.
  The default bailout test compares the magnitude or modulus of a complex
  variable to some bailout value:

  bailout test = |z| = sqrt(x^2 + y^2) >= 2

  As a computational speedup, we square both sides of this equation and the
  bailout test used by Fractint is:

  bailout test = |z|^2 = x^2 + y^2 >= 4

  Using a "bailout" other than 4 allows us to change when the bailout will occur.

  The following bailout tests have been implemented on the <Z> screen:

     mod:     x^2 + y^2 >= bailout

     real:    x^2       >= bailout

     imag:    y^2       >= bailout

     or:      x^2 >= bailout  or   y^2 >= bailout

     and:     x^2 >= bailout  and  y^2 >= bailout

     manh:    (abs(x) + abs(y))^2 >= bailout  (based on Manhattan metric)

     manr:    (x + y)^2 >= bailout

  The bailout test feature has not been implemented for all applicable
  fractal types.  This is due to the speedups used for these types.  Some
  of these bailout tests show the limitations of the integer math routines
  by clipping the spiked ends off of the protrusions.