The Mines of Moria(It’s a deep dark place where bad things happened)

Ocular Dominance

Araya, Joy, and Angela

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 200-600 m.

Interaction between different-eye-type synapses is stimulatory with the radius of 200-600 m.

The Difference EquationRandomize 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 FunctionThis is the 2nd derivative of the Gaussian

distribution with =0 and =20.

80022800

2222

630033239835.0329593425.1

kaka

ekae

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 withSpent much of our time waiting for

slow simulations: use the right tool