MClone
Encyclopedia
MClone, or Clonal Mosaic, is a pattern formation
algorithm
proposed in 1998 used specially for simulating giraffes and members of the Phelidae family of the mammalians. It was primarily proposed as a 2D model and lately was extended to 3D. An important feature of the algorithm is that it is biologically plausible.
Since the algorithm was created in order to address some of the problems with texture mapping
, its main goal is to produce, with the same set of parameters, a variable number of color patterns for a 2D or 3D object model. This way, for a relatively big amount of different entities represented by the same model, instead of using the same texture (and, doing so, each object would be equal to the others), one could use the different color patterns created by the MClone algorithm. Another useful feature of MClone is that it can be used to create patterns along with growing data of the object model.
Now that the model has the defined cells, and they are placed randomly, we want them to create a pattern. For this to happen, we make relaxations between all cells. We have two fundamental parameters in these relaxations: the mitosis
rate of each cell type (which indicates the delay in days for the cell type multiplication) and the adhesion rate of each cell type to the others (and to himself too). This last one is a number smaller than 1 that subtracts from the resultant force of the relaxation (thus, keeping the cells together).
Each relaxation happens has a defined "day" in which it occurs (this is the way MClone calls the relaxation process). The number of relaxations per day is defined at the beginning of the algorithm. The mitosis rate is defined as a number that indicates in how many days a cell is going to reproduce "again". For example, if the mitosis rate of a given cell type is 4, the cells of that cell type are going to reproduce itself in average each 4 days (i.e., for a cell born in the first day, it is reproducing itself in the fifth day, and in the ninth day, and so on).
Passed a given number of days, we are going to have a well defined pattern, which can or not be what we were waiting for. Although it could not seen intuitive through the explanation above, an important feature of the algorithm is that it is easy to predict how is going to be a pattern just after taking a look at the parameters passed to the algorithm.
Pattern formation
The science of pattern formation deals with the visible, orderly outcomes of self-organisation and the common principles behind similar patterns....
algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
proposed in 1998 used specially for simulating giraffes and members of the Phelidae family of the mammalians. It was primarily proposed as a 2D model and lately was extended to 3D. An important feature of the algorithm is that it is biologically plausible.
Since the algorithm was created in order to address some of the problems with texture mapping
Texture mapping
Texture mapping is a method for adding detail, surface texture , or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974.-Texture mapping:...
, its main goal is to produce, with the same set of parameters, a variable number of color patterns for a 2D or 3D object model. This way, for a relatively big amount of different entities represented by the same model, instead of using the same texture (and, doing so, each object would be equal to the others), one could use the different color patterns created by the MClone algorithm. Another useful feature of MClone is that it can be used to create patterns along with growing data of the object model.
The Algorithm
The MClone algorithm, essentially, works as follows: given the 3D model of the object which we want to create a new pattern, we first randomly place n cells on the model's surface. Each cell has a type, which defines many cell's properties, including its color. This way, for instance, if we want to simulate a pattern that has only two colors, it should be used just two types of cells.Now that the model has the defined cells, and they are placed randomly, we want them to create a pattern. For this to happen, we make relaxations between all cells. We have two fundamental parameters in these relaxations: the mitosis
Mitosis
Mitosis is the process by which a eukaryotic cell separates the chromosomes in its cell nucleus into two identical sets, in two separate nuclei. It is generally followed immediately by cytokinesis, which divides the nuclei, cytoplasm, organelles and cell membrane into two cells containing roughly...
rate of each cell type (which indicates the delay in days for the cell type multiplication) and the adhesion rate of each cell type to the others (and to himself too). This last one is a number smaller than 1 that subtracts from the resultant force of the relaxation (thus, keeping the cells together).
Each relaxation happens has a defined "day" in which it occurs (this is the way MClone calls the relaxation process). The number of relaxations per day is defined at the beginning of the algorithm. The mitosis rate is defined as a number that indicates in how many days a cell is going to reproduce "again". For example, if the mitosis rate of a given cell type is 4, the cells of that cell type are going to reproduce itself in average each 4 days (i.e., for a cell born in the first day, it is reproducing itself in the fifth day, and in the ninth day, and so on).
Passed a given number of days, we are going to have a well defined pattern, which can or not be what we were waiting for. Although it could not seen intuitive through the explanation above, an important feature of the algorithm is that it is easy to predict how is going to be a pattern just after taking a look at the parameters passed to the algorithm.