The trick is in the plant's numbers (and ages). When two plants are bred together, the lower numbered plant will always be on the left in the resulting seed/plant's lineage. So if you breed plants #12 and #8, and get plant #150, you will have #8 to the left of #12 on the lineage. Now, things can get tricky because if you breed #150 with plant #103, whose parents are #27 and #32, you will have #103 to the left of #150, which means that on the row below them, the plants will be ordered as #27, #32, #8, #12, even though #27 and #32 are obviously larger numbers.
That's what can make it confusing at times if you're trying to do symmetries and patterns, because (unlike, say, Dragon Cave) the plants don't have "male" and "female" identities or positions on their family trees, and are instead arranged by which plant is younger and which is older. So if you have a marvel fern whose parents are arranged with the male fern on the left and the marvel on the right, and you mate it with a male fern whose parents are arranged the same way, you might not get the pattern you expected and wanted if that male fern mate is actually older than your marvel fern. (And that's why, whenever I can, I like to mate two plants of the same variation to each other. Then it doesn't matter which one is older. )