A subgraph is formally defined to be what one gets by selecting just some subset of connections in a network—and with this definition Kuratowski's theorem must allow extensions of K 5 and K 3,3 where extra nodes have been inserted in the middle of connections.

For a long time it was assumed that the magnitude of the complexity was so great that it could never have arisen from any ordinary natural process, and therefore must have been inserted from outside through some kind of divine plan.

The following will update triples of cells in the specified order by using the function f : OrderedUpdate[f_, a_, order_]:= Fold[ReplacePart[ #1, f[Take[#1, {#2 - 1, #2 + 1}]], #2] &, a, order] A random ordering of n cells corresponds to a random permutation of the form Fold[Insert[#1, #2, Random[Integer, Length[#1]] + 1] &, {}, Range[n]]

When one sets up a quantum field theory one can typically in effect insert various mass parameters for particles.

The rule {2, 3}  {{{2, 1}, {1, 1}}, {1}} specifies that a new node should be inserted in the above connection, and this new node should have connections {Follow[list, i, {2, 1}], Follow[list, i, {1, 1}]} .

Devices like keyboards, mice and microphones convert input into data that is inserted into memory at certain fixed locations.

The picture below shows what happens if one repeatedly inserts circles to form a so-called Apollonian packing derived from the problem studied by Apollonius of finding a circle that touches three others.

It also has a polar plot of the positions of 14 pulsars relative to the Sun, with the pulsars specified by giving their periods as base 2 integers—but with trailing zeros inserted to cover inadequate precision.

Sometimes nonzero size is taken into account by inserting additional interaction parameters—as done in the 1950s with magnetic moments and form factors of protons and neutrons.