Cellular Growth B. Al Bahar, P. Giachini, H.J. Wagner Prof. Achim Menges, Ehsan Baharlou, Lauren Vasey
will form a very complex and differentiated structure by iterative application and recalculation. Different parameters govern the exact geometry of each offspring while random influences are not inherent. Furthermore different
Project Overview:
ways of feeding the cells can affect the general behaviour of the
Cellular Growth explores computational methods to simulate
structure. These are:
cell division processes found in Nature. A wide variety of intri-
Equal Feeding: All cells are given a fixed and equal amount of en-
cate geometries are grown by shaping simple beharviors. Su-
ergy every iteration. If a cell has enough amount of food it will split.
prisingly unusual systems are generated that are yet strangely
This method results in spherical structures, as the splitting of cells is
familiar to those found in our natural environment.
uniformely distributed. (Fig. 2) Feeding-Chain: The feeding of the cells takes place within a feed-
Inspired by works of Andy Lomas, Neri Oxman and nervous-sys-
ing-chain algorithm. Several cells are provided food and then will
tems a code-framework was programmed in which different
distribute the food along a food-chain to their neighbour cells.
systems of cellular growth can be investigated. The algorithm does
Target-Feeding and Surface Attractor: Similar to the Food-Chain this
not aim at simulating Mitosis and cellular division as it can be found
system distributes the food to the cells according to their distance to
in nature, but is yet closely related to its logics with the underlying
certain energy-spots. This algortithm also includes a logic to make
principle being the generation of basic rules and relationships that
the cells stick to a surface geometry, by being attracted to it.
Fig 2: An instance of a 24k Cell - Structure where all cells were feeded equally.
Fig 3: Optional Feeding-System, where only several cells are fed, These distribute the food along a feeding-chain to neighbour-cells.
Fig 4: Process of a feeding-chain structure over 3 timesteps. The gradient of the Mesh is based on the ‘age’ of the cells. White cells are youngborn.
Fig 5: The growing process can be influenced by a target-surface.
Fig 6a: Spring Target (Formula based on works by Andy Lomas)
Fig 6b: The cell tries to stay in equilibrium distance with all neighbour cells.
Fig 7a: Planar Target (Formula based on works by Andy Lomas)
Fig 7b: This Target makes the cell trying to stay in a plane with its neighbours.
Fig 8a: Bulge Target (Formula based on works by Andy Lomas)
Fig 8b: The Bulge Target moves the cell out of its planarity if enough pressure from the surrounding cells is applied.
Fig 9a: Collision Target (Formula based on works by Andy Lomas)
Fig 9b: The Collision Target makes the cell avoid other cells, that it is not directly connected to.
Fig 10: Post-processed geometry of a 11 Iteration offspring.
Project Methodology: The code is structured into to classes and follows an object-oriented
Planar Target: This drives the cell to try to stay as planar as possi-
approach: The Grid-Class stores all information and methods con-
ble with their direct neighbour cells. Therefore this target makes the
cerned with the overall network of cells while the Cell-Class deals
structure form a rather smooth outer surface.
with the functionalities of singular cells (splitting, moving, etc.).
Bulge Target: Opposing to the Planar Target, this algorithm takes
After a cell splits all its connections to neighbour cells are recalculat-
care of the cells having the opportunity to bulge out if a lot of pres-
ed, trying to make the number of connections for each cell uniformly
sure is put on them by the surrounding cells. In combination with the
distributed.
Planar Target this results in a wrinkled structure, that takes over as
Each timestep the cell undergoes several pressures and drives, that
much of the space as possible.
represent a physical simulation, similar to a particle-spring system.
Collision Target: The most simple to understand, still one of the most
These drives are represented in mainly 4 Targets, which comprise
important for cellular logics - the avoidance of collisions with other
partly opposing drives, that make the cell choose for which position
cells (excluding direct neighbours). A radius of influence governs the
it should take depending on an influence factor for each Target, that
distance that the cells try to stay away from each other. Obviously the
can be set by the user.
Collision Target becomes more and more relevant as two non-con-
Spring Target: The spring target simulates the cell’s behaviour of try-
nected cells are coming more and more close to each other. This
ing to stay in an equilibrium distance to all of its neighbours. The al-
algorithm is the heaviest of all, causing the most computational time.
gorithm is very much simplified for a quick calculation time and takes
After all Targets are computed, and multiplied by the user-defined
care of the cells forming a rather uniform mesh-typology.
Target-Factors, the new position is calculated and the cell is moved.