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4.2.1 Attraction force
Let a cell have the position .
The amount of direct neighbors of a cell may vary for different force calculations in the same iteration
Vol. 6 (2) / February 2019
4.2 Intercellular behaviors for linear and surface based simulations
a cell have direct neighbors with positions .
, Let a point or vector have the coordinates = , = ,.
,
The diameter of a cell, which equals the target distance between neighboring cells, be .
Let a cell have the position .
4.2 Intercellular behaviors for linear and surface based simulations
4.2.1 Attraction force
4.2 Intercellular behaviors for linear and surface based simulations
4.2 IntercellulaLarectbeaelhlcahevalilvoherasvfeodritrhleinecetpanoresaigtnihodbnsours.rfawciethbpaosseidtiosnims ula.tions
neighboring cells can be defined as being attracted to each other.
Let a cell have the position C.

,
The amount of direct neighbors of a cell may vary for different force calculations in the same iteration In order to achieve accumulations of cells that cluster together, rather than individual disconnected c

a cell have direct neighbors with positions .
The amount of direct neighbors of a cell m1ay vary−for different force calculations in the same
The amount of direct neighbors of a cell may vary for different force calculations in the same iteration.
=
iteration. Let a cell have n direct neighbors with po|siti−ons| P_r.

Let a point or vector have the coordinates = , = ,.

Let a point or vector have the coordinates = , = ,.
The diameter of a cell, which equals the target distance between neighboring cells, be . 4.2.1 Attraction force
The diameter of a cell, which equals the target distance between neighboring cells, be d.
In order to achieveInaocrcduemr utolaatciohniesvoefaceclulsmtuhlatiocnlussotef rcetlolsgethtahtecr,lursatehretrogthetahnerin, draivthideur athl adnisicnodnivnideucatel disconnected c cells, neighboring c4ne.e2lli.sg1hcbaonAribtntegradcetfililosnnecdafonarsbcebedienfgineatdtraascbtedingtoaettaracchteodthtoere.ach other.
1− neighboringcellscanbe d=efined as being attracted to each other.
,
,
with being an exponent which can be used to control diff,erent types of attraction forces. (Figure 3) The diameter of a cell, which equals the target distance between neighboring cells, be .
| − |
In order to achieve accumulations of cells that cluster together, rather than individual disconnected ce
1−
= | − |
with m being an exponent which can be used to control different types of attraction forces (Figure 3)
4.2.2 Repulsion force

with being an exponent which can be used to control different types of attraction forces. (Figure 3)
Figure 3: Attraction force 4.2.2 Repulsion force
with being an exponent which can be used to control different types of attraction forces. (Figure 3) keeping a certain distance between each other. This can be achieved by having an attraction force
In order to generate cell accumulations, cells need to be attracted to each other while at the same ti
In order to generate cell accumulations, cells need to be attracted to each other while at the same
distance becomes smaller than .
time keeping a certain distance between each other.This can be achieved by having an attraction
between neighboring cells while at the same time having a larger repulsion force between them if the
force between neighboring cells while at the same time having a larger repulsion force between them
if their distance becomes smaller than d.
1−
= | |
with m being an exponent which can be used to control different types of repulsion forces (Figure 4)
was used in the simulations by Hart and Lomas (Hart 2009, Lomas 2014). (Figure 5)
| − |
Figure 3: Attraction force 4.2.3 Spring force
4.2.2 Repulsion force
In order to generaFteigcuerlel a3c:cAutmtraucltaitoinonfosr,caelternatively to the attraction with repulsion for cells closer
In order to generate cell accumulations, cells need to be attracted to each other while at the same ti
than d, a spring force can be applied between neighboring cells with d as its rest length.This option
keeping a certain distance between each other. This can be achieved by having an attraction force
distance becomes smaller than .
4.2.2 Repulsion force
between neighboring cells while at the same time having a larger repulsion force between them if the In order to generate cell accumulations, cells need to be attracted to each other while at the same tim
keeping a certain distance between each other. This can be achieved by having an attraction force

Figure 3.
Figure 4.
Figure 5.
Attraction force
Repulsion force
Repulsion force
s smaller th1an . − = |−|

between neighboring cells while at the same time having a larger repulsion force between them if thei
distance beco
me
= | |
| |
1 −
| − |
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Cellular Design
Christoph Klemmt
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