Angiosperms (flowering trees) are more predictable in terms of their buds, because in addition to the terminal bud/s, in most cases a bud is also developed below a leaf petiole (stalk), and when that leaf falls off, the new bud grows from that position, known as the leaf axil (hence it’s known as an axillary bud). Therefore the bud pattern is equivalent to the leaf pattern or phyllotaxy.

It’s important to understand whether your tree has compound leaves, which have multiple leaflets.^ref These leaves only have one true petiole and at the base of this is where the lateral/axillary bud will form. No buds will form in the leaflet stems. See the below diagram.

Variables in the phyllotaxy include the number of leaves per node and whether they spiral around the stem or not. According to an article in Nature^ref, at the shoot tip itself, the ‘golden angle’ is observed between leaves: 137.5° – in the article the researcher finds that this angle minimises the energetic investment of creating divergent leaf positions (in the creation of vascular tissue to supply the leaves). After the stem elongates, leaves start to spiral according to the Fibonnaci rule, whereby common leaf spiral angles are 1/2, 1/3, 2/5, 3/8 and 5/13. For example a 3/8 would mean the angle between leaves is 3/8 of 360^o, or 135^o. This means it takes 8 spirals before a leaf is in the same position on the stem (although now vertically separated).

As can be seen above with only one leaf per node the arrangement simply spirals at different angles. With more than one leaf per node a similar principle applies but each pattern spirals (eg. both leaves in a two leaf per node spiral at the same angle). Multiple leaves at the same node is also called a whorl (common in gymnosperms).

So you should be able to predict where buds will develop on your angiosperm trees by simply looking at the leaf arrangement, and if it’s winter and your tree is deciduous, by the branch arrangement. What these buds will turn out to be – short shoots with flowers, vegetative shoots or flowers, is not as easy to understand but some pointers are here: Bud types – reproductive & vegetative.