Consider a smooth isotopy $f_t:M\to M$, where $M$ is some smooth closed manifold of dimension $d>1$, and $t\in[0,1]$. Assuming the dynamics of $f_0$ are “simple” and those of $f_1$ are "chaotic", can we say what is the likelihood of the bifurcation diagram of $f_0$ having a certain pattern? As proven by Masato Tsujii, probablistically, the answer is No. Specifically, we know it is impossible to define a "good" probability meeasure on the space of smooth functions which "sees" the size of generic families of maps similarly to how the Lebesgue measure "sees" the size of a bounded set. That being said, is there some other meaningful way to measure the size of different routes to chaos? In this talk we will show how Poincare's heuristic that periodic orbits are the "skeleton" of dynamical system can be used to tackle this problem. In detail, combining the ideas of J. A. Yorke, J. Mallet Paret and K. Alligood with elementary Graph Theory we will give a partial answer to this question by a counting argument. As we will prove, the answer strongly depends on the dimension of the manifold $M$. Specifically, we will show that when the dimension is high (i.e. $d>3$) there are infinitely many routes to chaos, all of which are, in some sense, equally likely. Conversely, we will prove the answer to the same question in low dimensions (i.e., $d=2,3$) reduces to the following two questions: 1. How many bifurcation diagrams for three-dimensional isotopies can be realized along a surface isotopy? 2. How many bifurcation diagrams for two-dimensional isotopies can be realized along a homotopy of interval maps? Time permitting, inspired by the ideas of Bo Deng, we will conjecture how these methods could be further developed, possibly to derive a universal bifurcation theory via the Rado graph. This talk is based on a joint project with Valerii Sopin from the SIMIS.