What this is a model of. This is an illustration — a mathematical model, not a picture of the brain or a measurement of it. The surface is a space of possibilities, and the ball on it is a system settling on a state within that space. The idea comes from active inference, a theory of brain function (Karl Friston and colleagues): a brain does not passively receive the world but continually settles on its best account of the current situation and its next action, by minimising one quantity — broadly, the gap between what it expects and what it senses. Here that quantity is drawn as height. Low points are states the system can come to rest in; the ball runs downhill into one of them, and that descent is an act of perceiving-and-acting reaching a resolution.
The basins are priors — expectations built from experience, the stored structure a system brings to a situation before it senses anything. Several compete at once. The frame of intention — the top-level goal the system is pursuing — shapes the landscape so that one basin becomes the deepest, and that is how an intention selects an outcome from the available possibilities. So the instrument models purposive settling: how an organism, given what it is trying to do, arrives at one perception or action rather than another, and how firmly it then holds to it.
You can set the frame yourself. Move the three precision sliders to deepen one basin and flatten the others; the act settles wherever you make the deepest well. Move Consolidation to switch the priors between deep and narrow — canalised, hard to shift — and wide and shallow, easily redirected, then use Sensory nudge to test which holds. Release the act to watch it descend, Live frame to let the surface change shape on its own; drag to rotate, scroll to zoom.
Formally, this is the free-energy landscape. Variational free energy is a mathematical function over the system's states, measured in units of information rather than physical energy; inference and action are gradient descent on its surface — the ball runs downhill to a minimum. The apex prior, the frame of intention, is what shapes the landscape: the priors already exist as competing basins, and allocating precision across them (the three sliders) deepens some and flattens others, so the act settles wherever the frame has made the deepest well.
The height is free energy in the statistical sense — the quantity this modelling minimises — not physical energy. It is information: a measure of how far the system's expectations miss what it senses, carried over from statistical physics by analogy and counted in units of information, not joules. The settling has two readings that should not be run together. In the illustration the ball comes to rest because its motion is damped — energy is drained from the ball's movement so it stops rolling, which is a mathematical operation on the picture, in information units. In the organism the same settling is realised physically: by the electrochemical activity of the neuronal structure — the anatomical, mind-brain interface — driving the bodily systems that carry out the act, work that is real and paid for in joules. How the model's damping and the body's electrochemical work relate is itself an open question; the surface depicts the information, while the body performs and pays for the act.
A second distinction — measured and felt. Separate from the information-and-joules question above, there is a second way of reading the one descent. Described from outside, the settling is gradient, precision, a stop-condition reached. Undergone from within, that same settling is the feeling — not a glow added once the act arrives, but what the coming-to-rest is for the system that is it. The Reading control switches only the vocabulary and the colour of the act; the surface and the descent are left untouched, because there are not two events here but one, read two ways. On this account feeling is not a further layer needing a ground beneath it — to look for one is to look for an inner agent one level down. The temporal arbitration that makes such settling necessary in the first place is developed in the companion instrument, The Chrono-loop.
Consolidation sets the character of each prior. A deep prior is a deep, narrow valley — canalised, in Waddington's term — and a sensory nudge cannot dislodge the act from it: the system is running on stored structure. A shallow prior is a wide, gentle basin, and the same nudge carries the act over a ridge into a neighbouring well, because the system is leaning on current data rather than stored expectation. Deep and shallow priors are not two mechanisms but two depths of one surface.
Moving the frame moves the thresholds. Under Live frame the precision allocation drifts, the surface changes shape, and the basin holding the act shifts beneath it. The ridge an activation must clear to reach another basin is the moving threshold, here drawn as terrain.
Two caveats. The surface shows a scalar height over two axes; the real landscape is N-dimensional — one axis per coupled system — so this is a projection, faithful to the structure but not to all the dimensions at once. And the parameters are illustrative: the picture is a sketch of the construct, not a measurement.
The single deepest point is itself a simplification. In the full system the act settles where many systems' moving, per-channel thresholds intersect, and that point is never absolute: it is relative and probabilistic — each threshold is set by precision, a statistical confidence rather than a hard line — because the coupled systems run continuously beneath it. The temporal cascade this landscape compresses — how an act starts, holds and stops — is developed in the companion instrument, Frame of Intention: Reaching for Coffee.