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In this paper, we show that patterns exist in the properties of the HighWater Mark (HWM) convergents of Champernowne's Constant in various bases (Cb),specifically in bases 2 through 124. The convergents are formed by truncatingthe Continued Fraction Expansion (CFE) of Cb immediately before the CFE HWMs.These patterns have been extended from the known patterns in the CFE HWMs ofChampernowne's Constant in base ten. We show that the patterns may be used toefficiently calculate the CFE coefficients of Cb, and to calculate and predictthe lengths of the HWM coefficients, the number of correct digits of Cb ascalculated by the convergent, and the convergent error. We have discovered thatminor corrections to the pattern formulations in base 10 are required for somebases, and these corrections are presented and discussed. The resultingformulations may be used to make the calculations for Cb in any base.

Analysis of the High Water Mark Convergents of Champernowne's Constant in Various Bases