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Continuous Maps on Digital Simple Closed Curves

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Figure

Figure 1. In 2exactly one coordinate and coincide in the other coordinate; since Z, each of the points p1 = (1,0) and p2 = (0,1) is both c1-adjacent and c2-adjacent to p0 = (0,0), since both p1  and p2  differ from p0  by 1 in p3 = (-1,1) is c -adjacent, b
Figure 2. 2results of the first step of the contraction: c -contraction of X , a digital simple closed 4c2 -curve, via H : X4×[0,2]ZX
Figure 4. A digital simple closed c1 -curve S= { }x7ii=0 and a ( ,c c11 -continuous map )f:SS such that f  is ( ,c c11) -homotopic to 1S
Figure 5. A simple closed c1 -curve C  and a covering by the digital line Z . Members of C  are labeled by their respective indices
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