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Geometry Shapes Evolution of Early Multicellularity

Figure 3

Degree capped tree growth.

A) A model of a growing tree with Node 0 at the center and a degree cap of 3. The numbers inside each node represent the generation of their birth while the colors denote the 3 different branches emanating from Node 0. The table below shows the total number of cells in each branch and the tree as a whole as a function of the number of generations. The number of nodes of each branch follow the same series: described by the recursion . This can be solved analytically to get . B) A model of a growing tree with a degree cap of 4. Similar to A) there is a recursive relationship for the number of nodes in a branch but it delves one more generation into the past, i.e. . For both trees the total number of nodes in the tree is twice the number in the red branch.

Figure 3