Applet
======

.. raw:: html

   <link rel="stylesheet" href="_static/edw_applet.css">
   <div id="edw-app"></div>
   <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
   <script src="_static/edw_applet.js"></script>

Exo-Daisy World, running live in your browser. The physics is the one pyEDW
integrates in Python: the dimensionless equations of motion of :doc:`theory`,
stepped with the same strong-order-1 stochastic Runge--Kutta scheme. Nothing is
precomputed; the daisies are the state of a stochastic differential equation
being solved as you watch. Drag the planet to spin it.

The applet is yours to take apart. It ships with the library as
`docs/_static/edw_applet.js
<https://github.com/EternalTime/pyEDW/blob/main/docs/_static/edw_applet.js>`_:
535 lines with no build step and no dependency beyond three.js. The first
hundred or so are the model itself - the growth window, the equations of
motion, and the stochastic Runge--Kutta step - ported line for line from
:mod:`pyEDW.model`. The rest is scenery.

Brighten the star and the black daisies, which warm the ground beneath them,
give way to white ones, which cool it. The shifting mix raises the planetary
albedo and reins the surface temperature back toward :math:`T_{opt}`. This is
the Gaian feedback\ :footcite:`lovelock1974` the model was built to exhibit. In
the plot, the green track pulls away from the bare-planet Stefan--Boltzmann
curve exactly where the biome is alive; drive the luminosity far enough in
either direction and the biome collapses, the track snapping back onto the
curve of a dead world.

The growth bandwidth :math:`\Delta T / T_{opt}` sets how fussy the daisies are
about temperature. Narrow it and the habitable band of luminosities shrinks to
a sliver; widen it and the biome clings on across the whole range.

Move the luminosity slowly and you will find the model is bistable: an
established biome survives at luminosities where a freshly seeded one dies out,
because a large standing population can hold the temperature where it needs it
while a sparse one cannot. This is why the ensembles in the
paper\ :footcite:`sowinski2025exo`, which sample a broad range of initial daisy
fractions, show life across a much wider band of luminosities than a single
small seeding would suggest. We take one liberty here. Since the growth terms
are multiplicative in :math:`f_B` and :math:`f_W`, zero is an absorbing state,
and a biome that collapsed could never return; the applet keeps a dormant seed
bank of :math:`10^{-4}`, too small to draw or to perturb a living biome, but
enough to recolonize a planet that becomes habitable again.

References
^^^^^^^^^^

.. footbibliography::