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Simple time-reversible systems can generate {\it irreversible} flowssatisfying the Second Law of Thermodynamics. Maps, and equivalent random walks,can also do this. We study a pair of time-reversible Baker Maps, $N2$ and $N3$,which generate dissipative{\it fractal} phase-space structures. Steadilydecreasing phase-space volumes correspond to the dissipation associated withentropy production. Like three smooth reversible dissipative one-bodyphase-space flows developed in the 1980s and 1990s our maps generate fractaldistributions, but in two dimensions rather than three, simplifyingvisualization and analyses. The continuity equation, which quantifiesphase-volume loss, motivates study of the fractals' reduced ``informationdimensions'', which were approximated by Kaplan and Yorke in terms oftwo-dimensional maps' two Lyapunov exponents. The maps studied here generatefractal (fractional dimensional) distributions in their phase spaces. Bymapping uniformly dense grids of points, fractal dimensions can be determinedby ``area-wise'' mappings. Beginning with a uniform grid area-wise mapping ofthe $N2$ Baker Map provides an information dimension of 1.78969. Alternatively,as many as a trillion iterations, starting from an arbitrary point, gives asmaller ``point-wise'' dimensionality, $1.741_5$. Neither of these preciselydetermined estimates matches the Kaplan-Yorke conjecture value, 1.7337. In thecourse of studying these three different approaches to information dimension wedeveloped random walk equivalents to both mappings, which greatly simplifiesanalyses. We found that for the older $ N2$ Baker map the three approaches alldisagree with one another! We later discovered that for the newer $N3$ Bakermapping the three approaches to information dimension, area-wise, point-wiseand Kaplan-Yorke, agree.

Random Walk Equivalence to the Compressible Baker Map and the Kaplan-Yorke Approximation to Its Information Dimension