Our algorithms are dealing with a 3D volume or surface. I am going to concentrate on the 3D mesh of vertexs, faces, and edges for this discussion.
Consider the problem of finding a maximum in a list of values. Serial code scanning from one end will easily find either the first or last of equal maxima, and get the same answer every time. Parallel code may find any of the maxima, and find a different one every time.
A similar problem is calculating an average. Floating point addition is not associative, (A+B)+C might differ slightly from A+(B+C). In serial code, the exact order of evaluation will differ depending on compiler optimizations. In parallel code it may differ depending on the number of threads, and the assignment of loop iterations to threads by the omp implementation.
A surface folding algorithm calculates a value for each point on a surface using floating point operations, and one of several almost identical values will be the fold point, resulting in different answers depending on very small differences.