is there a word for when the main structure of a plant is the same shape as a little part of it?

Answer 1

Branching would fit your concept. The trunk or stem splits into ever finer branches.
Each bud split occurs at a node and reflects the whole. While the apical bud continues to extend the lateral buds begin to grow and differentiate.

These also often reflect the Divine Proportion or Phi used is plant models.
http://www.td-grafik.de/artic/talk20030122/overview.html

Answer 2

fractals

the little bits are fractals of the main one