Progress Report No. 1

I present a simple model of a process that illustrates the following ideas:
A process has the following properties:
1. A series of changes with a goal. Usually the goal is a product.

  It might be regarded as stream of matter, or a channel through which products stream.
2. Is directed in space (and time).
3. Has inputs
(other processes) and an output (another process).
4. Death
:  1. A process disappears.
                 2. A process  hits another process (acts as its input). Both fuse and generate one or more processes (Birth).

The model might be the elementary process (unit) of a WOB computer. Its unit, or bit is 'change' represented here by a cell. The process (here the model) is the byte. Memory is part of the process.  Since each process manages its own time, WOB does not have a clock. Time is relative.

The model was developed with StarLogoT2001 R2.(The Center for Connected Learning and Computer based Modeling. Northwestern Unversity} It runs only on a Macintosh The model is written also in Mathematica. This version will be available for inspection in the future.

The unit consists of a stem cell (blue) and transitory cells (red, green and black). When stem cell divides  it creates a (green) transitory cell which is placed at the first location (loc = 1). The routine for stem cell division is called stem-mitosis. Since stem cell continuously divides its progeny advance (stream) upward. Some may divide again. They are called progenitors (red) . Cell division of progenitors is done by a routine called trans-mitosis. A third routine called shift-cells,  shifts cells upward. The three routines are called enzymes  They belong to  the stem cell. When cells reach the outer unit boundary, they die (black). Two boundaries determine the fate of transitory cells. prog-max demarcates the highest progenitor position. len-max demarcates the position where cells die.

Input: Only the stem cell receives  input (from the environment

  1. Resources, (mass and energy) for the maintenance of the unit.
  2. Demand of the environment for the product of the unit.

Output: Dead cells are the unit product and serve as output.

Only the stem cell receives and processes input (from the environment). Part of the processed input is inherited by its progeny. Information reaching the stem cell (resources and demand)  is stored in its chromosome. Both determine where len-max and prog-max will be  positioned. len-max[demand , resources] and prog-max[demand , resource], are updated during each stem cell division. Updated information is transmitted to the first progeny (loc = 1) which carries it upward.

time (or chronological system time) does not belong to the unit, and does not affect its behavior. It serves for unit monitoring by an observer.

The right image describes  some phases in the unit existence in the StarLogoT environment which is a matrix of 2000 x 2000 empty locations. At t-1 a stem cell is planted. This primordial stem cell which initiates   the events to come is called zygote (blue). Zygote remains in a dormant state until demand requires its output (dead cells). When demand rises, the unit unfolds . At t-2 demand has risen to 10, and at t-3, to 20 and so on. All this time  cells stream upward. As long as demand > 0 the unit flourishes. When demand = 0, zygote stops dividing and becomes dormant.  Only demand drives this unit. The unit survives even a destruction of  all transitory cells (green, red). It regenerates them all. Resources limit  unit performance, yet do not drive it, as demand does .

The right image of the unit above, highlights other properties of the unit.
stem-mitosis generates the main process.
trans-mitosis  generates secondary processes.
Each additional progenitor cell (red) generates a new process.
stores  long term memory. Transitory cells carry short term memory. How short term it is depends on demand and resources. Thus short term memory[demand, resources].

For instance, a cell a loc = 1 inherits prog-max and len-max. The unit remembers it as long as the cell lives, which depends on demand and resources. A cell at loc = n carries information generated by the stem cell n-time-steps ago.

As the unit evolves, chromosome is updated. It stores the unit configuration at a particular moment. Suppose that at time = n you took a zygote and planted it in an isolated environment. It will always generate the same unit. At each time step the unit will settle at the same attractor. Provided that the environment will accept the demand stored in the chromosome. On the other hand if environment enforces its own demand upon the unit (as the environment is expected to do), the stem cell will apply its experience to handle this new challenge (input).

Two zygote histories are depicted. The left one is a zygote history at a constant demand = 10. Each point is the (normalized) Euclidean distance of the current chromosome to the chromosome when zygote was first planted (t=1).. The right image depicts a zygote history when demand rose linearly from 1-60.