  Different methods for creating Olympic gels are analyzed using computer
simulations. First ideal reference samples are obtained from freely
interpenetrating semi-dilute solutions and melts of cyclic polymers. The
distribution of pairwise concatenations per cyclic molecule is given by a
Poisson-distribution and can be used to describe the elastic structure of the
gels. Several batches of linear chains decorated with different selectively
binding groups at their ends are mixed in the "DNA Origami" technique and
network formation is realized. While the formation of cyclic molecules follows
mean field predictions below overlap of the precursor molecules, an enhanced
ring formation above overlap is found that is not explained by mean field
arguments. The "progressive construction" method allows to create Olympic gels
with a single reaction step from a concentrated mixture of large compressed
rings with a low weight fraction short chains that are below overlap
concentration. This method, however, is limited by the difficulty to obtain a
sufficiently high degree of polymerization of the large rings.
