Limiting shapes for a non-abelian sandpile growth model and related cellular automata

Details Limiting shapes for a non-abelian sandpile growth model and related cellular automata Limiting shapes for a non-abelian sandpile growth model and related cellular automata

2010-06-25

arxiv.org/abs/1006.4928v2

Mathematics

Combinatorics

Revised version, to appear in Journal of Cellular Automata

Scientific paper

We present limiting shape results for a non-abelian variant of the abelian sandpile growth model (ASGM), some of which have no parallel in the ASGM. One of our limiting shapes is an octagon. In our model, mass spreads from the origin by the toppling rule in Zhang's sandpile model. Previously, several limiting shape results have been obtained for the ASGM using abelianness and monotonicity as main tools. As both properties fail for our model, we use a new proof technique: in our main proof, we introduce several cellular automata to mimic our growth model.

Affiliated with

Also associated with

No associations

Rating

Limiting shapes for a non-abelian sandpile growth model and related cellular automata does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Limiting shapes for a non-abelian sandpile growth model and related cellular automata, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limiting shapes for a non-abelian sandpile growth model and related cellular automata will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-309807