An experiment in using data flow programs to create animations.
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This experiment is done in Processing;
tested for Processing 2.2.1
under Windows 7 and Mac OS X 10.8.5.
Processing can be downloaded from
https://processing.org/

Processing 3 users see [Processing3.md](Processing3.md) note.

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For the "may_9_15_experiment"
the two example data flow graphs are contained in the source files
"may_8_graph.pde" and "may_9_graph.pde". By default the first graph is
used, it is a directed acyclic graph (does not contain loops).
For a short video recording 30 seconds of interactively working
with this program see https://youtu.be/fEWcg_A5UZc

To switch to the other one (which does contain a loop)
change what is commented out in the source file "may_9_15_experiment.pde".

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The "jun_21_15_experiment" is the first experiment with
dynamic data flow graph, a stream of data flow graphs
which are evolving using **almost continuous transformations**
and the program is executed while it changes on the fly in this almost
continuous fashion.

Clicking on the wavemaking nodes restarts a wave at the point of
click. The coefficients in the linear combinations are changed
by clicking on the
the controllers on the right of the images generated
as lienar combination for may_9 experiment,
and for jun_21 experiment those coefficients are controlled
by clicking on those images themselves (and by the script
which dynamically changes the program). Clicking and dragging
works the same as high-frequency multiple clicking
(try it not only for linear
combinations, but also for waves).

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The "jun_28_15_experiment" is the first experiment where the
data flow program contains itself in one of its own nodes.
Currently this is only used to facilitate visualization
of the dynamically changing program. But this is a start
of true higher-order stream-based programming, as the
node containing a data flow graph can be linked to
other nodes of this graph in the future.

For a short video recording 30 seconds of interactively
working with this program while it evolves (under
somewhat compressed timeline) see
https://youtu.be/gL2L7otx-qc

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These are some of the experiments for the line of research described
in the following preprint on linear models of computation:
http://www.cs.brandeis.edu/~bukatin/LinearModelsProgramLearning.pdf

The reference publication in the proceedings of GCAI 2015:
https://easychair.org/publications/paper/Q4lW

An essay describing the history of this project (Dec 2015):
http://www.cs.brandeis.edu/~bukatin/linear-models-of-computation-finally.html

The software architecture of May and June experiments is described in
this preprint: http://www.cs.brandeis.edu/~bukatin/HigherOrderDataFlow.pdf

Any questions or comments, feel free to e-mail to the first author
of these preprints.

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**August 5 - August 20 note:** It turns out that the architecture described
in our June experiments and July preprint can be modified to
eliminate even benign discontinuities resulting in
**continuous transformations** of software.

Moreover, this architecture allows to represent data flow graphs
of this class as **matrices of real numbers**.

We just posted a related software prototype implementing
some **continuous cellular automata**, "aug_20_15_experiment".

We expect to make one or more video previews available today.
Note that we cannot make those video previews quite faithful;
at the initial stage video compression software introduces
some distortion, then it notices the problems with quality
and offers to make enhancements, the result might be worse in
some aspects and better in some other aspects than the video
natively produced by the software.

The 30 second video for the default configuration is here:
https://youtu.be/KZHQxdZUlSU (see the page of the video for
a more detailed description).

The 30 second video for the second listed configuration:
https://youtu.be/rulK7l4jS-o (the one which we think has
a particularly high variability from run to run).

The 30 second video for the third listed configuration:
https://youtu.be/-pFil1_GEA4 (it might actually be the best
configuration, but I don't want to change the default right now,
in part because it is so unpredictable, and it's nice for
the default to be somewhat predictable).

The preprint describing this new development is available at
http://www.cs.brandeis.edu/~bukatin/DataFlowGraphsAsMatrices.pdf

(The preprints linked from this page are currently at the bottom of
http://www.cs.brandeis.edu/~bukatin/partial_inconsistency.html )

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**March 17, 2016 note:** This architecture is a generalization of
recurrent neural networks. This has a variety of implications:
http://arxiv.org/abs/1603.09002

**May 17, 2016 note:** This architecture is a convenient general-purpose
programming platform: http://arxiv.org/abs/1605.05296

**July 17, 2016 note:** More down-to-earth examples of general-purpose
programming in this architecture: http://arxiv.org/abs/1606.09470

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Supplementary materials for a talk at @party: [AtPartyTalk.md](AtPartyTalk.md)

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**August 15, 2016 note:** Remarks on linear and bilinear neurons in LSTM and gated recurrent unit networks: [Id_Mult_for_LSTM_GRU_MGU.md](Id_Mult_for_LSTM_GRU_MGU.md)

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**October 24, 2016 note:** Latest preprint covering pure dataflow
matrix machines and including our August 2016 experiments with
lightweight pure dataflow matrix machines in this repository: https://arxiv.org/abs/1610.00831

Latest presentation, "Self-Referential Mechanism for Dataflow Matrix Machines and Generalized Recurrent Neural Networks": (abstract: http://www.nepls.org/Events/30/abstracts.html#bukatin slides: http://www.cs.brandeis.edu/~bukatin/SelfReferentialDMMsOct2016.pdf)

New open source effort to implement Dataflow Matrix Machines in Clojure:
https://github.com/jsa-aerial/DMM

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**January 24, 2019:** [Processing Community Day in Boston](https://medium.com/fathominfo/pcd-boston-2019-734b11d8865f) (The [slides](https://github.com/anhinga/fluid/blob/master/ProcessingCommunityDayJan24-19.pdf) for my lightning talk, _Neuromorphic visual computations in Processing_)