CompuCell3d manual and Tutorial Version 2



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Figure 3. Calculating changes in the boundary energy and the volume-constraint energy on a nearest-neighbor square lattice.

For longer-range interactions we use the appropriate list of neighbors, as shown in Figure 4 and Table 1. Longer-range interactions are less anisotropic but result in slower simulations.



Figure 4. Locations of nth-nearest neighbors on a 2D square lattice and a 2D hexagonal lattice.




2D Square Lattice

2D Hexagonal Lattice

Neighbor Order

Number of Neighbors

Euclidian Distance

Number of Neighbors

Euclidian Distance

1

4

1

6



2

4



6



3

4

2

6



4

8



12



Table 1. Multiplicity and Euclidian distances of nth-nearest neighbors for 2D square and hexagonal lattices. The number of nth neighbors and their distances from the central pixel differ in a 3D lattice. CompuCell3D calculates distance between neighbors by setting the volume of a single pixel (whether in 2D or 3D) to 1.


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