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Larger than Life Automata

Larger than Life (LtL) dynamics were featured extensively on the Kitchen Shelf last spring, summer and fall. Recall that in these population models a birth occurs at cell x whenever the population of the neighbor set (including x) is in the interval [beta1, beta2] whereas a cell survives provided the neighborhood population is in [delta1, delta2]. The 8 demo experiments in this Java-based LtL simulator give a glimpse of the model's various phases, although many of the subtler effects described on the Shelf require arrays larger than are currently feasible (at acceptable update speeds) with current system-independent technology. For those, a dedicated simulator such as WinCA is required. The interface below is essentially the same as in our companion Greenberg-Hastings and Cyclic CA applets. For simplicity, all our demos use box neighborhoods, wrap edge conditions and a bright palette which keeps track of the number of updates since a live cell was born. Each of these settings may be changed in order to explore additional possibilities. Per usual, click on the number index of an experiment to go to its Table entry, and vice versa, or click on the Table's upper left # symbol to jump to the applet.

1. Conway's Life
Hit Start to see the original Game of Life emerge from symmetric randomness, with its characteristic blinkers and gliders. Click the title of this demo to go to Paul Callahan's excellent Life site, with more info about Conway's Game than you can imagine, including some very recent breakthroughs in computer-aided synthesis of exotic Life seeds.

2. A Range 3 Rescaling
Switch to the specified range 3 Larger than Life rule, with approximately the same proportions of the total neighborhood size as cutoffs for birth and survival. Again, starting from symmetric randomness, self-organization leads to blinkers and bugs (= gliders) amidst the 'seething gurp' which relaxes slowly to a final locally periodic state. Such threshold - range scaling, which continues to yield consistent complex dynamics for much larger neighbor sets, suggests that the proportions of Conway's game lie near a critical point in the asymptotic phase portrait. Click the title of this demo to read a recipe from the Shelf with more details, and a corresponding range range 10 example.

3. ... and its Period 31 Blinker
Load the initial image Period 31 to see some characteristic configurations from the same range 3 rule: a small blinker and bug, and a larger blinker with period 31 that is the featured thumbnail at the top of this page.

4. Range 2 Seething Gurp
Nearby parameter values in a large portion of LtL phase space give rise to a stable steady state of 'seething gurp.' In this range 2 example the gurp is barely supercritical, and so nucleates slowly to fill the lattice.

5. The Range 3 Exactly 6 Rule
Another collection of complex LtL dynamics are generated by the Exactly rules, in which a site is occupied next time if it has precisely a specified threshold number of occupied neighbors. Such systems only survive from initial states with low density, so start with the 1 in 10 image. Observe the resulting one-dimensional bugs and bug makers (= glider guns).

6. A Range 2 Bugmaker
Click on the thumbnail at the top of this page to see the trail generated by the initial seed of this experiment in a large space. In our small (100 by 100) array with wrap the resulting bugmaker interferes with itself, but there is still enough room to observe some of the 'skeeter' bugs which are jettisoned sideways at the core moves up.

7. Emergent Stalks in Range 2
Click this experiment's title to consult the original recipe for an LtL rule which generates stalks similar to those in range 1 Life without Death. Stalks only emerge from disordered states with a carefully chosen density, so our demo uses the 4 in 7 initial image.

8. Crystal Growth with Discontinuous Density
We conclude with a crystal growth example which may be viewed as a special case of LtL. Start from 7 ball to see a phenomenon we discovered only recently: the occupied set spreads linearly in time, but with a characteristic star-shaped region totally occupied within a surrounding stable convex region of density 1/2.

# Range [B1,B2] [D1,D2] Initial Condition
1. 1 3,3 3,4 Random
2. 3 14,19 14,23 Random
3. 3 14,19 14,23 Period 31
4. 2 11,18 6,18 Random
5. 3 6,6 6,6 1 in 10
6. 2 4,4 5,5 Bug Maker
7. 2 9,9 11,25 4 in 7
8. 2 1,25 16,25 7ball

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