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, restricted to centred fabric: centre-less farmsteads and hamlets never anchor growth Modified
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 at a fixed rate: the draw paces growth and varies the ensemble, and no longer decides how many centres appear Unchanged
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 new development may not shrink a park (a green area of at least the minimum park area, 2 ha default) below that area, whether by splitting it or by building along its edge [Min green span, Min park area] Modified: local rules
Every built cell keeps nature within T* Same, as a bounded walk whose destination must be a park; the check also applies to the newly built cell itself. The Green walk bounds the check during growth and at scoring, and both use the same park definition [Green walk] Unchanged in substance
New centralities seed near built land that has outgrown its centres, with probability 0.005 Released rather than drawn: each new home is charged to the centre it is nearest, and a centre earns its successor once that population reaches the service viability threshold, or once it can no longer grow. A seeding probability is uninterpretable to the person setting it and yields a different settlement count as window, cell size or growth rate change; people per centre is a planning judgement, and it is the figure the viability test already applies [Service viability] Modified: earned, not drawn
Isolated centralities seed on open land with probability 0.1 scaled by grid area No probability: a released centre may start away from existing development when the scenario allows detached settlements [Dispersed development] Modified: earned, not drawn
One walkable radius T* = 5 cells, cell side 1000/T* m, so T* ≈ 1 km Explicit metres throughout: cell size [Grid size] and four walking distances, defaulting to 1,200 m for centres, 400 m for green, and the 400 m stop and 1,200 m hub catchments that transit adds 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 occupy each settlement’s core, graded to a light edge [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 an unchanged 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 (fixed), protected green, unbuildable land including corridors carved from major roads, railways and rivers, centre areas, stops and stations Extension
All nature is available to build Developable land must be locally wide, and its region must either hold a viable settlement (the service viability threshold) or lie within the centre walk of an existing centre, where growth is served infill; all other open land is set aside as protected green before the run, so slivers and enclaves read as pocket parks Extension
Growth is spatially uniform in probability Transit shapes growth in two ways. Hubs (rail/tram stations, or points a planner designates) anchor a pinned mixed-use centre that seeds growth and survives post-processing. Corridors (bus stops, or a proposed route drawn as a line) attract growth: outside the stop catchment of a corridor and the wider hub catchment of a hub, the build and seeding draws are scaled by one minus the corridor preference, so growth concentrates along existing or proposed transit; the default preference is 0.35, and at 0 growth is unchanged [Corridor preference, Stop catchment, Hub catchment] Extension
Centralities stay where they seeded Post-processing offers centre options that all keep every home within the centre walk: as grown (locations untouched; a centre is added only where pruning removed a cluster’s serving centre), optimised placement (re-positioned central to the development served, added wherever new development lacks provision; existing centres serve the existing town and small infill within their walk, while a new district earns its own centre), and fewest centres (redundant ones removed while full coverage holds). Each settlement hosts an attached centre of its own; catchments cross green gaps, so nearby settlements pool their demand, centres below threshold demand are cut, growth without a viable centre reverts to nature, the centre audit verifies the result, and each centre is sized 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 in real-world use the model must deal 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. Pruning is the only post-processing step that removes population; the rest re-arranges what the run grew, and never adds anything. 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