One (useful) way to study three dimensional chaotic attractors is to define interval maps which behave similarly (and are often and are easier to analyze qualitatively), and then compare their dynamics and bifurcations with the numerical observations of the Differential Equation. Of course, chaotic attractors are not suspended one-dimensional maps, which raises an interesting question – can we explain analytically why their dynamics and bifurcations are described so well by one-dimensional maps? In this talk we will answer this question for the Lorenz attractor. As we will prove, one can rigorously reduce the butterfly attractor into a one-dimensional interval map which captures all its essential dynamics. Following that, using renormalization theory we will prove how one can use these results to give “topological lower bounds” for the possible complexity of knots realized as periodic orbits on the attractor. Based on joint work with Łukasz Cholewa.