The Mines of Moria (It’s a deep dark place where bad things happened) Ocular Dominance Araya, Joy, and Angela This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation In Slide Show, click on the right mouse button Select “Meeting Minder” Select the “Action Items” tab Type in action items as they come up Click OK to dismiss this box This will automatically create an Action Item slide at the end of your presentation with your points entered.

Visual information is transmitted from cells in the retina to cells in the visual cortex. Cells in the visual cortex receive nerve terminals from both right and left eyes. Competition occurs between the right synapses and the left synapses such that there exists spatial bands of cells responding to the right eyes interlacing with bands of cells responding to the left eyes. This is called the Ocular Dominance Column. Introducing the Question

At the Synapses Level Right Left Will I respond to right or left ?

The Rule Interaction between same-eye-type synapses is stimulatory within the radius of 200  m. Interaction between different-eye-type synapses is inhibitory within the radius of 200  m. Interaction between same-eye-type synapses is inhibitory with the radius of  m. Interaction between different-eye-type synapses is stimulatory with the radius of  m.

The Difference Equation Randomize initial condition for each cells So.. cell’s state (t+1) := cell’s state (t) + change Let Rn = fraction of the right synapses So, Ln = fraction of the left synapses = 1 - Rn

Defining Change The “change” depends on –The state of the neighboring cells Random initialization –The distance of the neighboring cells from the cell of interest. …. Using the Mexican Hat Function

The Mexican Hat Function This is the 2 nd derivative of the Gaussian distribution with  =0 and  =20.

Cellular Automata Simulator Made minor modifications to Tomas’ CA simulator for Maple ‘MexFlat’ placeholder

MexFlat Placeholder

It Worked!!! Beautiful striped pattern as excepted Right result – Wrong reason –We’re still using our ‘MexFlat’ placeholder function

Incorporating MexHat Right Reason, Wrong Result –No more stripes, everything to one state Right Tool, Right Result –The problem was lack of computational power –Took too long to run a large enough simulation –Neighborhood size of 81 cells

Absorbing Edges

Wrapping Edges

Conclusions Striped patterns arise from a variety of simulations Many parameters to play with Spent much of our time waiting for slow simulations: use the right tool