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    Metadata details:
    filename: FEP_Manifold.m
    path of file: ./repos/spm/toolbox/DEM
    
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% This demonstration routine simulates the emergence of life - as defined
% in terms of active inference - using a synthetic primordial soup. The key
% aspect of this dynamics is that there is a separation between dynamical
% states and structural states; where the dynamical states of the
% microsystem are equipped with a Lorentz attractor and the structural
% states correspond to position and velocity. The flow of structural
% states conforms to classical Newtonian mechanics. Crucially, the physical
% motion of each microsystem is coupled to its internal dynamics and vice
% versa; where the coupling among dynamics rests upon short range
% (electrochemical) forces. This means that the dependencies among the
% dynamics of each microsystem dependent on their positions. This induces a
% dependency of the systems structural integrity on its internal dynamics -
% which leads to biological self-organisation. This biological self-
% organisation is illustrated in terms of the following:
%
% i) the existence of a Markov blanket that separates internal and external
% states, where the internal states are associated with a system that
% engages in active or embodied inference.
%
% ii) emergent inference is demonstrated by showing that the internal
% states can predict the extent states, despite their separation by the
% Markov blanket.
%
% iii) this inference (encoded by the internal dynamics) is necessary to
% maintain structural integrity, as illustrated by simulated lesion
% experiments, in which the influence of various states are quenched.
%
%__________________________________________________________________________
 

    
function FEP_Manifold
% This demonstration routine simulates the emergence of life - as defined
% in terms of active inference - using a synthetic primordial soup. The key
% aspect of this dynamics is that there is a separation between dynamical
% states and structural states; where the dynamical states of the
% microsystem are equipped with a Lorentz attractor and the structural
% states correspond to position and velocity. The flow of structural
% states conforms to classical Newtonian mechanics. Crucially, the physical
% motion of each microsystem is coupled to its internal dynamics and vice
% versa; where the coupling among dynamics rests upon short range
% (electrochemical) forces. This means that the dependencies among the
% dynamics of each microsystem dependent on their positions. This induces a
% dependency of the systems structural integrity on its internal dynamics -
% which leads to biological self-organisation. This biological self-
% organisation is illustrated in terms of the following:
%
% i) the existence of a Markov blanket that separates internal and external
% states, where the internal states are associated with a system that
% engages in active or embodied inference.
%
% ii) emergent inference is demonstrated by showing that the internal
% states can predict the extent states, despite their separation by the
% Markov blanket.
%
% iii) this inference (encoded by the internal dynamics) is necessary to
% maintain structural integrity, as illustrated by simulated lesion
% experiments, in which the influence of various states are quenched.
%
%__________________________________________________________________________
 
% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging
 
 
% default settings (GRAPHICS sets movies)
%--------------------------------------------------------------------------
rng('default')
GRAPHICS = 1;
 
% Demo of synchronization manifold using coupled Lorenz attractors
%==========================================================================
d    = 8;
N    = 128;                         % number of (Lorenz) oscillators
T    = 2048;                        % number of time bins
t    = (T - 256):T;                 % final time indices
dt   = 1/32;                        % time interval
 
% parameters
%--------------------------------------------------------------------------
P.k  = 1 - exp(-rand(1,N)*4);       % variations in temporal scale
P.a  = rand(1,N) > 2/3;             % no out influences
P.e  = exp(0);                      % energy parameter (well depth)
 
 
% states
%--------------------------------------------------------------------------
x.p  = randn(2,N)*4;                % microstates (position)
x.v  = zeros(2,N);                  % microstates (velocity)
x.q  = randn(3,N)/32;               % microstates (states)
u    = zeros(1,T);                  % exogenous fluctuations
 
 
% illustrate dynamics from initial conditions
%==========================================================================
spm_figure('GetWin','Dynamics');clf
if GRAPHICS
    subplot(2,2,1)
else
    subplot(2,1,1)
end