Everything in the multiverse is made up of multiversal fields, which is an infinite-dimensional field that evolves locally over a "pseudotime". To beings inside universes, this multiversal field appears to always be in a steady-state, and can be characterised by their density.
Stable structures are those that evolve to zero density. Unstable structures are those that evolve to infinite density. Saddle structures are those that evolve to infinite density in some directions, and zero density in other directions. There is a hierarchy of saddles, from 0-saddles (stable) to ∞-saddles (unstable), representing different numbers of directions in which density is infinite.
Spiral structures (also known as oscillators) are those that exhibit periodic behaviour. From the inside of a universe, an oscillator is perceived as the pseudotime-averaged value of the amplitude of its fields; a nudge emitted from the universe interacts with the oscillator at all points in its period, propagates independently, and then the average of all these interactions is incident on the universe. There are no philosophical implications to this.
Chaotic structures are oscillators with infinite periods.