cate 1.1
Tool to draw the templates of chaotic attractors
Requires Python: >=3.10
Keywords: chaotic attractor, dynamical system, graph drawing, template

====
cate
====

|pipeline status| |coverage report|

CATE stands for **C**\ haotic **A**\ ttractor **TE**\ mplate.

``cate`` is a libre software tool (licensed under GNU Lesser General Public
License v3.0 only) to draw the templates of chaotic attractors.

.. SPDX-License-Identifier: LGPL-3.0-only


Chaotic attractors are solutions of deterministic processes, of which the
topology can be described by templates.  We consider templates of chaotic
attractors bounded by a genus-1 torus described by a linking matrix.

This tool first validates a linking matrix by checking continuity and
determinism constraints.
The tool then draws the template corresponding to the linking matrix, and
optimizes the compactness of the representation.  The representation is saved
as a Scalable Vector Graphics (SVG) file.


Citation
--------

``cate`` is developed as a research project.

The motivation for a tool such as ``cate``, an introduction to linking
matrices, and a description of the optimization logic are described, *inter
alia*, in a publication presented at the conference Graph Drawing 2018.

This publication is available in the conference proceedings
(`doi:10.1007/978-3-030-04414-5\_8 <https://doi.org/10.1007/978-3-030-04414-5_8>`__, paywalled),
or on arXiv (`arxiv:1807.11853 <https://arxiv.org/abs/1807.11853>`__).


If you use ``cate`` for a publication, please cite as follows:

  Maya Olszewski, Jeff Meder, Emmanuel Kieffer, Raphaël Bleuse, Martin Rosalie,
  Grégoire Danoy, and Pascal Bouvry.
  **Visualizing the Template of a Chaotic Attractor.**
  In *Graph Drawing*, volume 11282 of Lecture Notes in Computer Science, 106–119.
  Springer, 2018.
  `doi:10.1007/978-3-030-04414-5\_8 <https://doi.org/10.1007/978-3-030-04414-5_8>`__.

Or you may use, at your convenience, the following
`BibTeX entry <https://gitlab.inria.fr/cate/cate/raw/master/doc/OlszewskiM2018Visualizing.bib>`__:

.. code-block:: bibtex

   @inproceedings{OlszewskiM2018Visualizing,
     author    = {Olszewski, Maya and
                  Meder, Jeff and
                  Kieffer, Emmanuel and
                  Bleuse, Rapha{\"{e}}l and
                  Rosalie, Martin and
                  Danoy, Gr{\'{e}}goire and
                  Bouvry, Pascal},
     title     = {{V}isualizing the {T}emplate of a {C}haotic {A}ttractor},
     booktitle = {Graph Drawing},
     series    = {Lecture Notes in Computer Science},
     volume    = 11282,
     pages     = {106--119},
     publisher = {Springer},
     year      = 2018,
     month     = sep,
     doi       = {10.1007/978-3-030-04414-5_8},
     isbn      = {978-3-030-04413-8},
   }


Installation
------------

``cate`` is packaged as a regular Python package, and is published on
`PyPI <https://pypi.org/project/cate/>`__.  It hence can easily be installed
with ``pip``.

For more details on how to install a Python package, one can refer to
https://packaging.python.org/tutorials/installing-packages/

The latest stable (recommended) version can be installed with the following
command (assuming ``pip`` is installed):

.. code-block:: console

   $ pip install cate

----

It is recommended to use a virtual environment to install ``cate``.  Again, one
can refer to https://packaging.python.org/tutorials/installing-packages/ to get
a more comprehensive overview.

On a typical Linux environment, the typical commands to use would be:

.. code-block:: console

   $ python3 -m venv cate_venv
   $ source cate_venv/bin/activate
   $ pip install cate

This will create a new virtual environment in the ``cate_venv`` subdirectory,
and configure the current shell to use it as the default ``python``
environment.  This will then install ``cate`` in this new environment without
interfering with the already installed packages.

One would then exit this environment either by exiting the current shell, or by
typing the command ``deactivate``.

Further uses of ``cate`` only require to activate the virtual environment with
the following command:

.. code-block:: console

   $ source cate_venv/bin/activate


Usage
-----

Given a linking matrix, we can draw its template with ``cate`` by following
these steps.  For instance, let's consider the following linking matrix:

.. image:: https://gitlab.inria.fr/cate/cate/raw/master/doc/5x5_001_matrix.png
   :align: center
   :alt: 5x5 linking matrix

This linking matrix describes a template made of five strips.  ``cate`` uses
JSON files as an input.  A linking matrix has to be described as an array made
of arrays of integers, with a row-major order.  For the above example linking
matrix, one can encode it as follows.  Note that whitespaces, new lines, … are
insignificant, but do improve the readability.

.. code-block:: json

   [[2, 1, 0, 0, 0],
    [1, 1, 0, 0, 0],
    [0, 0, 0, 0, 0],
    [0, 0, 0, 1, 1],
    [0, 0, 0, 1, 2]]

To draw the compact template of this example linking matrix, it is as simple as
calling ``cate`` with the name of the input file as the first argument.

.. code-block:: console

   $ cate 5x5_001.json
   [  INFO  ] Input matrix
   [  INFO  ]   [2, 1, 0, 0, 0]
   [  INFO  ]   [1, 1, 0, 0, 0]
   [  INFO  ]   [0, 0, 0, 0, 0]
   [  INFO  ]   [0, 0, 0, 1, 1]
   [  INFO  ]   [0, 0, 0, 1, 2]
   [  INFO  ] Starting constructing the tree
   [  INFO  ] Maximum possible template length: 2
   [  INFO  ] Finished constructing the tree
   [  INFO  ] Starting creation of the SVG template
   [  INFO  ] Shortest template
   [  INFO  ]   Level 1: (0, 1), (3, 4)
   [  INFO  ] Finished creation of the SVG template

``cate`` has created a SVG whose default file is ``template.svg``.

.. image:: https://gitlab.inria.fr/cate/cate/raw/master/doc/5x5_001_template.svg
   :align: center
   :width: 500px
   :alt: template of the 5x5 linking matrix

----

The comprehensive set of elementary matrices of size 5x5 and 6x6 is available
in the official repository of ``cate``
(see https://gitlab.inria.fr/cate/cate/tree/master/examples).
The depicted example corresponds to the
`5x5_001.json <https://gitlab.inria.fr/cate/cate/raw/master/examples/5x5_001.json>`__
linking matrix.

The comprehensive list of the supported options and their usage is available by
typing ``cate -h``.

.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..

.. |pipeline status| image:: https://gitlab.inria.fr/cate/cate/badges/master/pipeline.svg?style=flat-square
   :target: https://gitlab.inria.fr/cate/cate/commits/master
   :alt: pipeline status

.. |coverage report| image:: https://gitlab.inria.fr/cate/cate/badges/master/coverage.svg?style=flat-square
   :target: https://gitlab.inria.fr/cate/cate/-/jobs
   :alt: coverage report