Table 1. Agreement between the sets of predecessor knots and the sets of subknots observed in KnotPlot and ideal configurations with increasing numbers of crossings. For most of the analyzed knots, all observed subknots in the disk matrices of KnotPlot and ideal configurations belong to the set of predecessor knots of the corresponding global knot type. However, as the crossing number increases some of the KnotPlot and ideal configurations have subknots that are not predecessor knots of the global knot type. When one considers majority subknots (i.e. subknots that achieve at least 50% frequency in some subarc using our closure algorithm), then all of these subknots belong to the sets of predecessor knots of the corresponding global knots. If one concentrates on the knot types forming predecessor knots of the first generation then they are visible as subknots in the disk matrices of the KnotPlot and ideal configurations of the corresponding global knots.

	number of crossings	3	4	5	6	7	8	9	10
	# alternating knot types with predecessors	1	1	2	3	7	18	35	92
KnotPlot	all subknots ⊆ predecessors	1	1	2	3	7	16	27	58
	some subknots ∉ predecessors	0	0	0	0	0	2	8	34
	all majority subknots ⊆ predecessors	1	1	2	3	7	18	35	92
	first generation predecessors ⊆ subknot set	1	1	2	3	7	18	35	92
	all first generation predecessors ⊆ majority subknot set	1	1	2	3	7	18	32	78
	some first generation predecessors ∉ majority subknot set	0	0	0	0	0	0	3	14
Ideal	all subknots ⊆ predecessors	1	1	2	3	7	18	35	89
	some subknots ∉ predecessors	0	0	0	0	0	0	0	3
	all majority subknots ⊆ predecessors	1	1	2	3	7	18	35	92
	all first generation predecessors ⊆ subknot set	1	1	2	3	7	18	35	92
	all first generation predecessors ⊆ majority subknot set	1	1	2	3	7	18	35	92