Splitting and Merging Processes

Several flame modes exhibit cell splitting and merging. Cell motions in these modes are considerably more complex, and the correct mapping of cells in a given video frame to their descendents in the next frame is challenging. Once cell ancestry is determined, we use time-line representations to follow splitting and merging histories. Three examples of split-merge processes with different characteristics are presented below:

4-5 Melting: This relatively simple example of splitting and merging is found close to the point where the ordered 4-cell state loses stability.

12-6-1 Disordered State: This experiment was performed just beyond the point at which the 12/6/1 ordered becomes unstable. The ring structure of the central cell surrounded by 6 cells in a hexagonal array is still visible. Much of the splitting activity occurs in the cells in the outermost ring.

9-3 Heteroclinic: This state is representative of intermittent behavior observed with heteroclinic connections. A stable pattern (usually 9 cells surrounding 3 cells) appears for an unpredictable amount of time and then disorganizes.

For a discussion of methods of tracking splitting and merging processes see:
Tracking cell splits and merges
J. A. Withers and K. A. Robbins
Proc. IEEE Southwest Symp. on Image Analysis and Interpretation (1996) pp. 117-122.

For a more complete discussion of the time line visualization see:
Cell Mapping: Tracking Splits and Merges in Large-scale Evolving Structures
Jo Ann Withers, Master's Thesis, University of Texas at San Antonio, May 1996,
Supervising Professor: Kay A. Robbins.

For a discussion of the underlying physics of the intermittency observed in heteroclinic connections see:
Identification of intermittent ordered patterns as heteroclinic connections
E. Stone, M. Gorman, M. el-Hamdi and K. A. Robbins,
Physical Review Letters 76 (1996) pp. 2061-2064.