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math.CO2021
On some explicit integrals related to "fractal foothills"
Anton A Kutsenko
In the previous papers, we tried to analyze the complete loop counting functions that count all the loops in an infinite random walk represented by digits of a real number. In this…
nlin.CD2021
On some explicit integrals related to "fractal mountains"
Anton A. Kutsenko
Loop counting functions estimate the number of "weighted" loops in a digital representation of . Roughly speaking, each is considered as an infinite walk, wh…
nlin.CD2021
Fractal mountains and binary random loops
Anton A. Kutsenko
We discuss a variation of Takagi curves based, however, more on algebraic than geometric principles. Namely, we construct functions of loops in a special binary representation. The…