We can then conceive all the intricacies of tangency.
"The Concept of Nature" by Alfred North Whitehead
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The advantage of working with random walks of packings, rather then with simple random walks of their tangency graphs, is that there exist non-trivial harmonic functions associated with them which have a geometric interpretation.
Random walks of circle packings
Clearly, for s, a generic curve with a point of an inverse self-tangency (see 5.1.1), there is a unique T − -equivalence class associated to it.
Arnold-type Invariants of Curves on Surfaces
It maps t− ∈ T − to such t− ∈ T − , that there exists s (a generic curve with an inverse self-tangency point), for which [s− ] = t− and [s− ] = t− .
Arnold-type Invariants of Curves on Surfaces
C ⊂ T − be the set of all the T − -equivalence classes corresponding to generic curves (from C ) with a point of an inverse self-tangency.
Arnold-type Invariants of Curves on Surfaces
When we go along this path we see a sequence of crossings of the self-tangency and of the triple point strata of the discriminant.
Arnold-type Invariants of Curves on Surfaces
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