Model Iteration Iteration means to repeat a process and is sometimes referred to as looping. In ModelBuilder, you can use iteration to cause the entire.

Model Iteration• Iteration means to repeat a process and is sometimes

referred to as looping.

• In ModelBuilder, you can use iteration to cause the entire model to iterate, or just iterate an individual process

Model Iteration• Feedback

– Feedback is where the output of a process is made the input to an earlier process. You can declare a variable as feedback by opening the properties of the input variable and selecting the output variable that will feed back as the Input, as shown below.

– You can also use the Connect tool and connect an output variable to feed back to an input variable.

Model Iteration• Iteration variables

– ModelBuilder provides two variables that contain the current iteration number and the current list index.

%i%— the current position, or index, in a list variable. The first position is zero.

%n%— the current model iteration. The first iteration is zero. Use with Series or Counts.

You can use these variables in calculations and pathnames. For example, the pathname of an output dataset might be:

E:/Data/Result%i%_%n%

Model Iteration

Cellular automata (CA) have their foundations in the specification of digital computers. They were pioneered by Alan Turing, John von Neumann, and Stanislaw Ulam, initially as computing media. Later, they have been adopted by other fields outside of computing and put to a wide variety of applications.

Today, CA is often refers to dynamic (i.e. change over time) modeling in a 2 dimensional space based on a set of rules.

Cellular Automata

Cellular automata model consist of several key components:

• Cells arranged evenly on a tessellated grid-space (i.e. a raster)

• Cell states

• Neighborhoods,

• Transition rules, and

• Time.

The cell space in a cellular automaton is assumed to be both uniform in structure and infinite in extent (infinity is generally achieved by describing the cell space as a torus: its edges 'wrap around' on themselves; again, the cell space does not have to be infinite in extent).

The individual cells in a cellular automata model are occupied at any given time by a discrete state, (e.g., full or empty, alive or dead, yellow or blue, one or zero). In a landscape context the cell state can be made to represent any attribute of the environment, e.g., land use (residential or commercial), density (high density or low density), land cover (forested or concrete), etc.

Each cell in the cellular automata has a neighborhood of adjacent cells that surround it. Neighborhoods are commonly characterized as either being 'Moore' (the cell in question and the eight surrounding cells that border it) or 'von Neumann' (the cell in question and its four cardinal neighbors), as the diagram below illustrates. However, a neighborhood can be specified to represent any form.

Rules are defined that govern the state of any given cell in the matrix at any given time in the evolution of the model.

These transition rules are applied to cells synchronously, altering the state of cells according to their individual condition and the condition of adjacent cells in the neighborhood.

The transition rules assume that time in cellular automata is discrete. It proceeds in iterative steps, 'jumping' from one point to the next: t; t+1; t+2; t+3; ...; t+n.

One of the most famous sets of transition rules in John Conway's Game of Life.

In the Game of Life, cells are considered to be 'alive' (their state is coded as ‘1’) or 'dead‘ (‘0’).

In each iteration (i.e. time interval) of the model, transition rules are applied to the cells' states.

A 'live' cell in one iteration remains 'alive' in the next iteration if its neighborhood contains either two or three other alive cells, otherwise its state is coded as 'dead'.

Additionally, a 'dead' cell in one iteration can become 'alive' in the next if its neighbourhood contains exactly three 'live' cells.

The home work assign this week is variation of the game of life with the rules:

Birth Rule

If [Cell State is “Dead” in time t]

and if [# of cells in cell state “alive” in neighborhood >1]

then [set state of cell “alive” in time (t+1)]

End

Death Rule

If [Cell State is “Alive” in time t]

and if [cell state has been “alive” > 3t]

then [set state of cell “dead” in time (t+1)]

End

Lab 15: CA Modeling

Results

Model Rules

• In the first simulation infestation will be 99% exclude from Forest Type 1; 95% excluded in Forest Type 2, and 100% excluded in the vegetation types 3, 4, 5 and 6.– Risk = Con(veg2 == 1, 0.99, veg2 == 2, 0.95, veg2 > 2, 1)

• Infestation area will die out after 4 time steps and will be unable to infest new areas.

• Insects will only travel 500 meters in one time step.– Potential = Con (distsource == 0, 0, distsource <= 500, 1,0)

• If an infested cell is over 4 time increments old it will be “Killed.”

• Combine source, potential, risk and random to determine if a cell will be infested in the time step. – Newsites = Con(potential == 1 and random > risk and Source < 1,

Source + 1,0)