Principle

We'll start with a spectral representation of the logistic equation.

Here it is - spectrum for R = 2.573 :

This spectrum corresponds to a near harmonic sound - near, because the fundamental is missing.

Now let's reverse this graph :

And let's consider it as an audio file (a time / amplitude representation instead of the frequency / amplitude representation) :

... this is an impulse response corresponding to a multi-tap delay !
( a series of consecutive Dirac impulses)

So : if we take the spectrum of an oscillator, export it as an audio file, it makes an impulse response for a convolution reverb.

This is confirmed when comparing :
- an impulse response taken from a real room (Church Buiksloterkerk in the Nederlands)

- the spectrum got from one of the behaviours of the Lorenz system, converted into an audio file :

OK, this is a multi-tap delay :

Another multi-tap delay, slightly more exotic.
Reading from the right to the left : "tac tac TAC tac tac tac tac" :

Now, a mix of delay / reverb - in other words, first reflections / diffuse field :
( keep on reading from the right to the left )

A mix of two "taps" and bursts of diffuse field :

A first loud reflection, then plain diffuse field :

Pure diffuse field :

The principle described above leads to mono -> mono impulse responses.
We want to produce mono -> stereo (2 files) , and stereo -> stereo (4 files) impulse responses.

This is possible if we change the initial conditions of the oscillator : generation of IRs with the same global aspect but different details.

But, only the chaotic parts are subject to the "initial condition sensivity".
The harmonic behaviour is not a chaotic one, thus will always be the same even if changing the initial conditions.
So :
- the "Dirac / reflection / delay" parts of the IR will always be mono->mono
- the "noisy / diffuse field" parts of the IR, on the other hand can be mono->stereo and stereo->stereo