Neighbour-Sensing model is the proposed hypothesis on how forms and shapes arise in the world of fungi.Audrius Meskauskas and David Moore in 2004.
The hypothesis suggests that each hypha (thread) in the fungal mycelium generates certain abstract field that (like the known physical fields) decreases with the distance. For instance, to distribute the hypha more evenly, the hyphal tips should avoid each other and threads in general. It is possible to rephrase this as "hypha generate scalar field that hyphal tips to avoid". When hypha follow this rule they form round ball with the close to uniform density inside. Even such a simple structure does not form as a result of the purely random branching and growth. The exact nature of the field may be important by itself but knowing it is not necessary for building the model. It is similar to the case of the harmonic oscillator where the same equations also describe processes that appear completely different (spring, pendulum and electric circuit).
The first truly interesting shape emerges after adding the rule that the tips try to preserve certain (for instance, 45 degree) orientation in the field of the Earth gravity. "Avoid tips and threads" plus "try to keep 45 degree orientation" together results a cone that is largely an empty inside and quite similar to some most primitive fruit bodies.
Chord production is possible after assuming the existence of the vector fields that are parallel to the vector of the hyphal threads. This looks like quite a big assumption, however researchers have observed the similarly oriented electric currents in hyphal surroundings. These currents enter or exit the hyphal tip and run in parallel to the rest of the thread, gradually entering it back at more basal phase. If such current can orient the growth direction of other tips ("parallel tropism"), all numerous tips in mycelia at the end turn in a or at most several alternative directions, building something that looks like a twisted wire rope. This "rope" can get more dense (and similar to the real chord) if we additionally add a weak positive attraction that presses the tips stronger together. Fungi use chords to transfer food resources over larger distance, or to spread to the new areas of growth, and also stems of the usual mushrooms look quite a bit similar.
It is also easy to make a colony "flat" by introducing tropism toward horizontal plane. This allows to compare the simulated morphology with the actual morphology observed in Petri dishes, where fungi mostly grow on the surface. While flat, the colony stays three dimensional: crossing hypha do not go directly through each other, resulting more realistic picture than in simple two dimensional models tried in the past.
The Neighbour-Sensing model explains how various fungal structures may arise without supposing any kind of the growth regulating hormones. These hormones, playing important role in plant and animal development, cannot be found in fungi.
Interestingly, it is possible to find some parallels between neighbor sensing model and mathematical models of flock. Flock algorithms also frequently contain components of the positive and negative attraction to the neighbor (responsible for the forming of the flock that has stable density) and desire to fly same direction as other members of the flock (similar to the parallel tropism). The main difference is that flock equations rely on the "mass center" of the flock, assuming than birds (or other creatures) can easily determine it. Fungal tips have no vision and unlikely to be capable to determine such center precisely, so the model instead assumes that they only sense the closest neighbours, and the capability to sense rapidly declines with the distance.