mathematical field atom in prysm
renders a particle that is a field — a function assigning values to every point in a domain. a leaf in the element tree (leaf type: field). distinct from all other particle atoms: field content is not stored pixel data but a continuous mathematical object evaluated at render time
scalar field: one value per point (temperature, density, rank). vector field: one vector per point (flow, force, gradient). the domain may be 2D, 3D, or the cybergraph itself
protocol role
field is a leaf in the element tree $\mathcal{T}$ (§7 of prysm/layout). leaf type: field. it has no sub-organelles. its membrane constrains the viewport into which the field is projected. the field itself is defined over an unbounded domain; the viewport clips it
sizing
all values in spatial quanta $g$
| parameter | sizing type | values | default |
|---|---|---|---|
| src | — | particle CID or inline definition | required |
| width | fix or fill | any $k \cdot g$ or fill | fill |
| height | fix or fill | any $k \cdot g$ or fill | fill |
| domain | — | 2d, 3d, graph | 2d |
| resolution | — | low (g), medium (g/2), high (g/4) | medium |
$s_{min} = (8g, 8g)$
field types
| type | values per point | examples |
|---|---|---|
| scalar | single float | cyberank density, token price gradient, network activity |
| vector | direction + magnitude | link flow, force field, gradient descent |
| complex | magnitude + phase | probability amplitude, wave interference |
| tensor | matrix per point | stress field, curvature field |
render modes
| mode | field type | rendering |
|---|---|---|
| heatmap | scalar | continuous color gradient — min→max maps to emotion palette |
| contour | scalar | isoline bands at equal value intervals |
| flow | vector | streamlines following field direction |
| arrows | vector | arrow glyphs sampled at grid points, length = magnitude |
| magnitude | vector/complex | scalar heatmap of the magnitude only |
| phase | complex | hue encodes phase angle, brightness encodes magnitude |
default mode: heatmap for scalar, flow for vector
emotion and color
field color IS emotion applied to the value range. the field's minimum value maps to the low end of the active emotion color, maximum to full saturation. the tri-kernel drives the emotion signal; the field maps that signal continuously across its domain
a cyberank field: high-rank regions glow with joy green (#00fe00), low-rank regions dim to near-black
states
| state | visual change | trigger |
|---|---|---|
| default | rendered at current resolution | src loaded |
| loading | glass placeholder, pulse $1\text{s}$ | src resolving |
| computing | overlay shimmer | field evaluation in progress |
| error | vector [broken-field, $4g$, anger] | src failed |
state transitions: $150\text{ms}$ ease
3D
in the 3D extension (§11 of prysm/layout):
- 2D field renders as a plane at the membrane's $p_z$
- 3D field renders as a volumetric region; the neuron can enter and look around
- vector fields in 3D render as particle streams (flow lines as animated ion trails)
ECS
- Entity: field organelle
- Components:
Sizing { width, height }FieldSrc { Particle(cid) | Inline(FieldDef) }FieldDomain { D2 | D3 | Graph }FieldType { Scalar | Vector | Complex | Tensor }FieldRenderMode { heatmap | contour | flow | arrows | magnitude | phase }FieldResolution { low | medium | high }LoadState { loading | computing | loaded | error }Emotion { color }— drives value-to-color mapping
- System:
FieldSystemevaluates field at render resolution, writes framebuffer region