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For example, parent has excircle radii equal to 2, 3 and 6. These are precisely the inradii of the three children , and respectively.

If either of or is applied repeatedly from any Pythagorean triple used as an initial condition, then the dynamics of any of , , and can be expressed as the dynamics of in

:

which is patterned on the matrices' shared characteristic equation

:

If is applied repeatedly,

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