Classical and digital homotopy classes

In this paper, we examine the relations between classical homotopy groups, digital fundamental groups of L. Boxer [6], and digital homotopy classes on the digital wedge products of pointed digital diamond (or square) circles. We demonstrate that the classical homotopy groups of pointed functions from a wedge product of homotopy simple closed curves to itself may differ completely from the digital homotopy monoids consisting of the classes of NP_u pointed homotopic functions from the digital wedge product of pointed digital diamond (or square) circles to itself under the κ-adjacency relations on Z² for κ=4,8 and u∈{1,2}.