Unfortunately only organisms with very, very simple nervous systems have been mapped. Things like the hydra (which is Cnidria, something like a stationary jellyfish) and everybody's favorite worm the c. Elegans have been mapped out, but both of these are so simple they're more like nervous 'nets' than systems.

Besides that we don't even have a reliable enough model of a single nerve cell, since nervous cells are extremely diverse in size, morphology, electrical properties and spiking patterns.

There are some crazy scientists at MIT (lead by Sebastian Seung) trying to automate the process of mapping an entire mouse brain by using robotics to slice and image processing algorithms to reconstruct the connectivity between cells. I am skeptical of this kind of project because it seems way out of the realm of reasonable numbers to compute; mammalian cortical neurons make around 10,000 connections to other neurons, and 1 cubic mm contains maybe 100,000 of such cells.

It would be much more productive to do some of your own research regarding what has already been done toward this goal. It may feel like you are the first computer science major to be interested in neuroscience, but I assure you there are thousands of computer literate theoreticians and experimentalists hard at work. The brain is much more complicated than you imagine, even if you consider nervous systems that lack a defined brain.

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Aplysia Californica is a very well understood animal. Although the entire map of the nervous system hasn't been made, scientists know the most about its basic memory encoding neurons, and the parts of the nervous system that are mapped are manipulated in experiments. The mapped regions are theoretically enough for you to perform your biological determinism experiment. It has ~20,000 neurons in its nervous system and is one of the animals we use in our lab. Scientists even know which specific neurons are used for recalling/learning certain memories such as its retracting reflex. That is as close to fully mapped and understood that I know of. The zebrafish is a close/distant second depending on your definition of "greatest detail."

Hope that helps.

Edit: Defined "very well understood animal."