Which interference effects occure, if we use an inhomogenuous, but continuous space, having a velocity function dependent of the location? To understand the things, we use a wave field reconstruction discussed in the simulation chapter. Normally it is supposed that the (delay-) distance *dt* between any location *(x,y,z)* and a channel source point *(x0,y0,z0)* is a linear function (velocity *v*) of the geometrical distance *ds* given by

*dt = ds/v*

with

*ds = sqrt((x-x0)² + (y-y0)² + (z-z0)²) = sqrt(dx² + dy² + dz²)*

We know, that a single neuron has very different dendritic and axonal diameters at different locations, thus signals have very different speeds within different parts of the trees. Also the neural tree is not expanding straight linear. Thus, the dependency between geometrical distance *ds* and delay-distance *dt* can be seen non-linear. Because the possibility to solve large neural networks in time domain numerically is not even realistic in the moment, it is suggested, that any (deterministic or stochastic) function *f* of the actual location modifies the delay distance *dt* in a non-linear, analytical matter.

*f = f(x,y,z,x0,y0,z0), {f} = {-1...1}*

*dt = (f/F + 1) ds/v, {F} = {positiv, +1...+oo}*

The quotient *f/F* we call distortion (in percent). For large *F* the influence of the term *f/F* disappeares. May be *f* is sinoidal periodic in *dx* and *dy* to get the following distorted fields.

The pictures give an impression, which effects occure, if we use inhomogenuous spaces to reconstruct interference projections. The same example is given several times as a wave field movie on different inhomogenuous delay spaces. The pictures may be seen as a part of an interference integral.

Note, that the interference events (waves meet eachother at special locations -> interference integral) appeare distorted in the same way.

Note also the possible encapsulation of waves in circles! This may be the only possible way, to interfere onto one neuron by a single channel (axon) in case, a neuron has some thousand synapses placed over a space greater the wavelength of incomming impulses.

Comment: In the minute the downloadable version of PSI-Tools is only useable to simulate homogenuous fields.

Four channel wave field (PSI-Tools simulation) projected in a homogenuous space (part of a wave field movie)

Same as above, but projected in a rippled, inhomogenuous space 5%

Same as above, but in inhomogenuous space 10%

Same as above, but in inhomogenuous space 15%. Note a new interference on a single location

Same as above, but in inhomogenuous space 20%

Same as above, but in inhomogenuous space 25%

Same as above, but in inhomogenuous space 30%

Same as above, but in inhomogenuous space 40%

Same as above, but in inhomogenuous space 50%

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Access No. since jan. 2, 1997