Cellular Earth

According to Gaia Theory , the Earth is not just
a complex ecosystem, it is a super-organism . Earth
has a protective atmosphere with an unlikely
balance of gases which can only be explained by
way of some self-regulating system. Earth's
biosphere is self-organizing and works in such
a way as to keep its systems in some kind of meta-
equilibrium, broadly conducive to life.

We humans are recently-developed cells within the
super-organism, and we are beginning to behave
like a cancer. The fever called Global Warming is
a call for us to reduce our footprint and find a more
integrated and balanced relationship with
the other cells of Earth.

Cellular Earth Animation
The animation above was created as a celebration of Earth Day 2006. It is a Java applet. On a fast computer it should run at about 30 fames per second.

This is a spherical Cellular Automaton . Cellular automata are typically arranged on a Cartesian grid in 1, 2, or 3 dimensions, which makes it easy to compute neighbor-cell interactions. This animation uses a spherical model, which is a non-Euclidean surface. The propagation of dynamical patterns happens in-the-round, including the back-side of the sphere.

The cell positions are arranged on the sphere as follows: First, twelve points are arranged in a regular, icosahedral pattern. Then a method for increasing the geodesic frequency is applied, whereby every pair of neighboring points gives birth to a new point lying in-between the pair. The number of points is increased to 42. This process is applied four times to make a total of 2562 points. This is equivalent to the recursive subdivision of the triangles of an icosahedron to generate a geodesic dome.

Unlike a flat surface, points on a sphere do not tessellate with perfect regularity. This is illustrated by the geometry of geodesic domes, in which some vertices have five connecting neighbor vertices, while all others have six. The resulting regions of five-fold symmetry correspond to the twelve vertices of the icosahedron (there can also be octahedral, tetrahedral, cubic, etc. geodesics).

Neighborhoods
The Game of Life is the most popular cellular automaton, which uses 9-cell neighborhoods. But hexagonal grids have been used, as well as many others. In this spherical model, every neighborhood has either 5 or 6 cells - each cell corresponding to a point (vertex) on the geodesic surface. Neighborhoods are calculated based on proximity of points after each step of increasing the geodesic frequency. When the final geodesic frequency is finished, the local neighborhood of each cell is stored in memory. This is used to apply the cellular automata rules.

The Rules
The interesting thing about cellular automata is the rules - the manner in which cells change their states as a result of their neighborhood states. The rules in this technique are similar to those described in "Gliders and Riders", a chapter in the forthcoming book, Stigmergic Optimization. A Java applet showing this technique can be found here: http://www.ventrella.com/Alife/Cells/GlidersAndRiders/Cells.html . The details of this technique will also be published in the Artificial Life X conference proceedings in 2006.

Evolving Rules
The rules are represented as a set of parameters - "genes" - and evolved using a genetic algorithm. To find rules which create interesting space-time patterns, the genetic algorithm has an interactive component, such that a human can provide the fitness metric. A random population of individuals (represented as cellular automata rules) are generated. Then the results of randomly-selected rules are viewed and ranked as either good or bad. While the cellular automaton is running, at semi-regular intervals, randomly chosen cells have their states randomly changed. This provides some stimulation, so that interesting dynamics can emerge. The individuals with a good rating have a higher chance of mating with other high-ranking individuals, using crossover and mutation. The fitness values of the entire population are decayed over time, with each viewing, so that aesthetic trends that may have been ranked high in the past are allowed to fade (if they have been given a good ranking, then their genes have already propagated into the present population anyway). This technique was also used to evolve 2D Cellular automata, and also Mandelbrot imagery to approximate faces.

Artistic Motivation
Cellular automata have an appeal to the mathematical mind. But also the dynamics can be visually striking, and evocative of natural processes. Small narratives emerge from the primordial soup.

Global warming is a concern to many of us. Solutions to our status as Earth's skin cancer must be sought, and they must be deep solutions - by way of a paradigm-shift in all humans in terms of our impact and role in the health of the planet. Humans evolved thinking that land was infinite. But we live on a sphere. What goes around, comes around - the impact of human civilization is global. This understanding must happen on many fronts - scientifically, politically, and aesthetically. The Gaia Hypothesis of James Lovelock and Lynn Margulis can be a starting point. If nothing else, it is a poetic expression that gives us a narrative - it makes a good story. I choose to believe it.

The creation of this spherical cellular automaton - rendered in Earth tones - is a way for me to share my vision of Earth as an exquisite super-organism - made up of interacting cells.

Bucky Fuller's Dymaxion Map

Geodesic grid used for climate modeling
by Randall, Ringler, Heikes, Jones, and Baumgardner

"Many people fear that ecocide has now come to overshadow
nuclear war and emerging diseases as a threat to global civilization."
- Jared Diamond, Collapse page 7

"Our planet's immune system is trying to get rid of people."
- Kurt Vonnegut, A Man Without a Country , p 104.