Currently Martijn is pursuing his master's degree in biomedical physics at Amsterdam University. Apart from biomedical physics, he also has a strong interest in theoretical physics and tries to combine both fields whenever possible. With a small group of people from his university, he makes educational material about science for children.
Modeling Folding Caused by Growth
In nature there are systems that will fold while growing. Here I look at a model that captures some of the basics of this behavior using only a simple set of rules. I compare the results to observations in biology and chemistry, in particular to folding caused by cell growth and molecular bonding.
The model is based on a network substitution system. There are two different types of nodes, represented by black and white. The black nodes are active and can divide into three new nodes creating a new cell. A totalistic rule determines how nodes are substituted.
The cell representations in this model are simple surfaces that are bounded by edges and have no internal edges. The shape of the cells is not preserved during the evolution. Cells must have similar dimensions, so cells are rescaled by connecting their centers of mass with all their nearest first neighbors. The connections are then laid out in three-dimensional space using a spring model. This is then used to construct the 3D shape.
Rule chosen: 260
In the space of left-handed, range-1/2, four-color CA I like rule 260 because it is exactly the same as rule 60 from the ECA. For any binary initial condition, rule 260 is the smallest of a superset of 1048576 rules that all have this behavior. The largest rule number in this set is 4294963460. The set is formed by taking all the possible numbers ##########010010 from base 4 (# is a number in range 0-3). When you plot the table of numbers without sorting them you can see the pattern caused by the base for the enumerating system.