Isobenefit Urbanism

Theory: the published model and this implementation

The plugin’s growth rules descend from D’Acci’s published Isobenefit Urbanism model. This page records where they are unchanged, where they differ, and why. The introduction covers the pipeline around the rules.

The published model

Isobenefit Urbanism (D’Acci 2019) proposes settlements whose benefits are distributed evenly: wherever one lives, a local centre with shops and services, and open green land, are both within a walking distance. The iso means equal. D’Acci formalised the idea as a cellular-automaton morphogenesis, published as the Isobenefit-cities simulator (D’Acci and Voto 2023) with Python code by Michele Voto. The automaton grows a grid of land cells from seeded centralities under a small set of rules, so that the walkability guarantee holds at every step no matter how large the settlement becomes.

The published model works on an abstract grid: every cell starts as nature, distances are measured in cells, and the walkable radius T* is about one kilometre, described as a 15-minute walk (later summaries give one to two kilometres). Each simulation step scans the grid; a nature cell adjacent to built land may become built if a centrality is within T* and the move would not break the nature rules; new centralities seed stochastically; each built block draws a population density; the run stops at a population cap.

The rules

Each row gives a rule of the published simulator, what this implementation does, and a status: unchanged (same rule), reparameterised (same rule, different units or defaults), modified (behaviour differs), or extension (no counterpart in the published model). Parameter names in brackets are the plugin’s settings.

Published rule This implementation Status
Build only on nature cells adjacent to built land (periphery growth) Same: a candidate must be empty and touch built land Unchanged
A centrality must be within T* of the new cell, measured as straight-line distance A centre must be within the centre walk, measured as a bounded walk over the grid that cannot cross unbuildable land [Centre walk] Modified: walkable distance
Build with probability 0.5 once the checks pass Same mechanism; the default is 0.25 [Build probability] Reparameterised
Nature remains one connected region, and every nature strip stays at least T* wide Local rules instead: no green corridor between developments may be pinched below the minimum span (a strip bounded by water or a carved road corridor is exempt, so land beside a barrier can be built right up to it), and a build that splits green must leave each fragment a minimum contiguous area [Min green span] Modified: local rules
Every built cell keeps nature within T* Same, as a bounded walk; the check also applies to the newly built cell itself. During growth the radius is the larger of the two walks; the Green walk applies at scoring [Green walk] Unchanged in substance
New centralities seed near built land that has outgrown its centres, with probability 0.005 Same trigger; the probability is fixed at 0.01, at most one new centre seeds per iteration, and seeding stops at 80% of the population target Modified: added guards
Isolated centralities seed on open land with probability 0.1 scaled by grid area A per-cell probability without area scaling, exposed as Off, Moderate or Aggressive [Dispersed development] Reparameterised
One walkable radius T* = 5 cells, cell side 1000/T* m, so T* ≈ 1 km Explicit metres throughout: cell size [Grid size] and two walking distances, defaulting to 800 m for centres and 400 m for green Reparameterised
Each built block draws a density from three tiers at fixed probabilities (0.7, 0.3, 0) Same draw; tiers and shares are settings, and post-processing then arranges the drawn values so the highest sit nearest the final centres [Development density] Unchanged draw, extended placement
Run stops at a population cap (500,000 default) Same stop; the target counts new residents only, since existing fabric is treated as served by its own centres [Target population] Modified: new-only accounting
Cells are scanned in a fixed raster order against a frozen copy of the grid Cells are visited in a shuffled order each iteration, which removes the scan-direction bias Modified
One run, one output Ensembles: many runs blended into likelihood layers, with the best single run selected as the scenario Extension
The grid starts as uniform nature Real inputs from OpenStreetMap: existing built fabric (frozen), protected green, unbuildable land including corridors carved from motorways, railways and rivers, centre areas, stops and stations Extension
Centralities stay where they seeded Post-processing re-positions centres central to the development they serve, adds one wherever new development lacks a centre of its own (existing centres serve the existing town, not new growth), culls redundant ones, and sizes each by the population in its catchment Extension
Distances are straight lines over an abstract plain One metric for growth and scoring: bounded walks over the grid, blocked by unbuildable land. Street-network distances were tried and removed, since a new settlement’s streets do not exist yet and a network metric measures new and existing fabric on different terms Modified: walkable distance

Most of the modifications have one motivation: the published model assumes a uniform abstract plain, while real places arrive with fragmented green, rivers, motorways and existing towns.

Where the automaton ends and post-processing begins

The growth rules above produce the raw grown state, which the plugin always saves. Everything else is post-processing on that state: pruning stranded settlements below the minimum size, re-positioning and sizing centres, arranging the drawn densities, scoring runs, and selecting the best. The walkability guarantees are enforced by the growth rules during the run; post-processing improves the presentation and the centre arrangement without adding or removing population. The recommended-plan notes document that pipeline.

Terminology

Centrality is D’Acci’s term for a local centre of shops and services among homes; the plugin’s interface says centre and treats the words as synonyms. Morphogenesis refers to D’Acci’s growth model specifically. Isobenefit describes the goal: equal benefit wherever one lives. The run report states the achieved coverage.

Sources