Gradient Demo¶

The Gradient demo showcases the most fundamental building block in aggregate computing: the G block, which computes a self-stabilising distance field from source devices.

What It Shows¶

Shortest-path distance propagation across a network
Self-stabilisation: the field converges from arbitrary initial states
Convergence speed proportional to network diameter

Building Blocks Used¶

Block	Role
G (gradient)	Computes minimum-hop distance to source

How It Works¶

One device is designated as the source (device 0 by default). The gradient block runs on every device:

def gradient_program(ctx):
    is_source = ctx.sense("is_source")
    return gradient(ctx, is_source)

Each round, every device:

Sources output 0.0
Non-sources collect distance estimates from neighbours, add the physical distance to each neighbour, and keep the minimum

Formally:

\[ G(\delta, \text{src}) = \begin{cases} 0 & \text{if src} \\ \min_{n \in N} \left( G_n + d(n, \delta) \right) & \text{otherwise} \end{cases} \]

where \(N\) is the set of aligned neighbours and \(d(n, \delta)\) is the Euclidean distance.

Convergence¶

The field stabilises in \(O(\text{diam})\) rounds, where diam is the network diameter (longest shortest path). On an 8×8 grid with spacing 1.0 and comm_range=1.5, convergence typically takes 10–12 rounds.

The convergence chart in the simulator tracks the maximum change across all devices per round. When this value drops to zero, the field has stabilised.

Network Configuration¶

Parameter	Default	Effect
Topology	Grid	Regular lattice for predictable propagation
Rows / Cols	8 × 8	64 devices
Spacing	1.0	Unit distance between adjacent devices
Comm Range	1.5	Each device sees its 4 direct neighbours (and diagonals at distance √2 ≈ 1.41)

Interpretation¶

The colour map shows distance values:

Purple / dark — low distance (near source)
Yellow / bright — high distance (far from source)

The resulting field forms concentric "rings" around the source, similar to a topographic map. This gradient field is the foundation for many higher-level patterns: channels, data collection, broadcasting, and leader election all build on top of it.

Self-Healing¶

Try removing devices (click "Remove Random Device") after the field has converged. The gradient automatically recomputes through alternative paths — this is the self-stabilisation property in action.

Try It¶

Select Gradient from the demo dropdown in the simulator, or try it on the live deployment.