The arena

A fly has no representation of a portfolio. It has a representation of where it is. So the market is built as a place, the fly is left to navigate it the way it evolved to, and where it ends up is read back out as an allocation.

Five mesas

Each tokenized stock is a mesa: a flat-topped plateau standing in a valley, drawn the way the rest of the site is drawn. The five sit at fixed positions on the valley floor and never move. What changes is what they look like.

Height and hatching are not two views of the same number. A mesa can be tall and barely hatched, which is a price that has moved on nothing, and it can be low and almost solid, which is heavy trade going nowhere. The two axes are kept separate because conflating them is the more flattering mistake.

Erosion

When a mesa’s volume falls away it does not disappear between one tick and the next. Its height is its momentum smoothed backwards over the preceding ticks, and the weight given to each past tick decays faster the less volume the mesa has had. A mesa nobody is trading wears down over minutes into a low, faintly drawn shelf, and builds back if volume returns.

This is the idle state, and it is deliberate. A market that goes quiet should change the shape of the terrain the fly is standing on, because that is the only channel through which the market can reach it at all. An instantaneous mapping would make quiet stocks flicker in and out of the landscape and make the walk jitter for reasons that have nothing to do with the fly.

Getting the terrain into the eyes

The fly does not receive prices. Each tick, the arena is rendered from the fly’s own position and heading into a one-dimensional luminance profile across azimuth. A near mesa occupies more of that profile than a far one, a tall mesa occupies more of it than a short one, and dense hatching darkens the bins it falls in. The bin count belongs to the retina and is reported by it: not yet measured.

That profile drives the photoreceptor inputs, which feed the retained medulla output layers, which feed the ring neurons of the ellipsoid body. Ring neurons inhibit, so a bright bin suppresses the part of the ring that faces it. This is the same pathway that lets a real fly hold a heading against a visual landmark; here the landmarks are the mesas.

Heading and turn

The EPG population forms a ring attractor. A single bump of activity sits somewhere on the ring and that location is the fly’s heading. Self-motion shifts the bump; visual input through the ring neurons pins it. The bump is not read out and reinserted by us — it persists because of the recurrent structure already in the graph, and the committed heading is where the population vector points at the end of the tick.

PFL cells compare the current heading against the activity in the fan-shaped body and project asymmetrically to the two lateral accessory lobes. The difference in firing between left and right becomes a turn: the descending neurons receiving that asymmetry drive the body one way or the other. The committed headingDelta is that turn. Forward speed is a function of how well the heading matches the goal direction, so a fly that is pointed wrong walks slowly and mostly turns.

Escape

DNp01 — the giant fibre — sits outside all of this. It is a looming detector, and when the profile expands fast enough it fires. When it fires the fly bolts off the cliff edge, the walk stops, and the book goes flat in the same tick. There is no threshold we tune per market; it is the same detector responding to the same kind of stimulus it responds to in the animal.

Position becomes allocation

The fly’s position on the valley floor is converted to weights by inverse distance to the five mesas, raised to the power 2, softened by 0.02 so that standing on a mesa does not divide by zero, and normalised so the five sum to one. The mesas sit 72° apart on a ring of radius 0.72 and never move; only their height and hatching change.

Two consequences follow directly and neither is incidental. Standing still trades nothing: if the position does not change, the weights do not change, and no swap is submitted. And every rebalance is a walk — the book cannot jump from one corner of the simplex to another, because the body cannot teleport across the valley. The turn rate of the fly is the rate limit on the portfolio.