As reflected in their traditional notations—and emphasized by Venn diagrams— And ( ∧ ), Or ( ∨ ) and Not correspond directly to Intersection ( ⋂ ), Union ( ⋃ ) and Complement . If one starts from the single-element set {1} then applying Union , Intersection and Complement one always gets either {} or {1} . And applying Complement[s, Intersection[a, b]] to these two elements gives the same results and same equivalences as a ⊼ b applied to True and False .

With this setup, each step then corresponds to LifeStep[list_] := With[{p=Flatten[Array[List, {3, 3}, -1], 1]}, With[{u = Split[Sort[Flatten[Outer[Plus, list, p, 1], 1]]]}, Union[Cases[u, {x_, _, _}  x], Intersection[Cases[u, {x_, _, _, _}  x], list]]]] (A still more efficient implementation is based on finding runs of length 3 and 4 in Sort[u] .)

An example studied since antiquity involves finding lengths or angles using a ruler and compass (i.e. as intersections between lines and circles).

Note also that the intersection of the past and future light cones for two events separated by a distance x in space and t in time always has a volume proportional exactly to c 2 t 2 - x 2 .

To obtain such trimmed networks one can apply the function TrimNet[net_] := With[{m = Apply[Intersection, Map[FixedPoint[ Union[#, Flatten[Map[Last, net 〚 # 〛 , {2}]]]&, #]&, Map[List, Range[Length[net]]]]]}, net 〚 m 〛 /.

The geometrical pattern was presumably made by first constructing 48 regularly spaced spokes by repeated angle bisection, as in the first picture below, then drawing semicircles centered at the end of each spoke, and finally adding concentric circles through the intersection points.