How the maps were made

The maps show 66 complexity paradigms – 50 research programmes and 16 disciplines – in 7 families, and 202 influences between them. It uses two kinds of data. Qualitative information about each paradigm and its connections is based on editorial judgement and named works; the reasoning for each entry is recorded beside the data. Quantitative data about the scholarly literature, books and institutions shows how far each programme’s ideas were taken up and how generative it was, i.e. how much new work of note it produced. Both kinds of data inform and complement each other.

The paradigms

A research programme is a community working on shared questions and methods. It has founding works, people who carry it on, and institutions, journals or meetings of its own. A single thinker without such a community is not a programme, however important: Cilliers and Juarrero appear on the map as people linked to programmes, and Helmholtz as the source of one programme’s key idea.

A discipline – statistical mechanics, game theory, operations research, Earth system science – is a whole field with its own chairs and journals. The programmes drew on the disciplines, but a discipline is not itself a complexity programme. The disciplines are all ongoing, and no view draws a measurement of them.

The 7 families (Mind & Cognition, Cybernetics & Systems, Social & Organisational Complexity, Complex Systems, Dynamics & Self-Organisation, Ecology & Earth Systems, Symbiosis & Relational Ontologies) group paradigms by lineage: who learnt from whom, in which setting and on which topics. A discipline sits with the programmes it is most tied to. The families are a reading aid. Their boundaries are not sharp.

Start, peak and end

A paradigm starts with its founding paper, book or institution – for ecological anthropology, Geertz’s Agricultural Involution in 1963. For a programme, start, peak and end mark its generative phase, the years in which it produced new core work; the uptake that follows shows in the river. They follow the measured lifecycle (below), each within a measured range: a programme starts with its founding work while its measured emergence can begin within five years of it, and key works older than its start are its ancestors.

Each range comes from two redrawings. Each of the programme’s key works is left out of its canon in turn, since one work more or less moves the emergence or the peak by three years or more for 21 of the 50 programmes; and the judged samples and yearly counts are drawn again 200 times, as for the end. A date the record gives stays where it lies in its range, else it takes the range’s year closest to it. The range reaches two years past what the redrawings give on either side.

A programme’s generative phase ends when its new work of note has fallen to a small part of what it was, and stays there. The end is read from one count alone: the programme’s core works among the most cited tenth of their year and subfield, per million works of its home fields, so that the growth of the literature does not keep an old programme alive. Its height is its best ten-year average. The programme has ended once that count has stayed below a third of its height for five years, and is ongoing while its last five measured years average a third or more. Drawing the judged samples and the yearly counts again 200 times gives a range of years for the end. The record takes a year inside that range, by default the nearest five years to the measured decline. Where the measurement is unsure – fewer than four in five of the redraws agree – or rests on fewer than about one such work a year, the record takes the year in the range closest to the date its sources give, and stays ongoing only where the measurement allows it. Three programmes depart from the rule, each with its reason beside it. Gaia theory is ongoing, because new work entered it after the years its few counts give. Complexity economics is ongoing, with new statements in reviews and books that the counts miss and part of its later work counted under econophysics. Second-order cybernetics ends in 1985: its counts rise only from the 1990s, when the name spread retrospectively, and so measure its later uptake more than its generative phase.17 of the 50 programmes have ended.

The peak is the measured peak, the years of a programme’s greatest generative output, within its range. Every programme’s peak lies in its range.

Significance, from 0 to 10, rates a programme’s weight at its peak. It follows the programme’s rank by its highest uptake: where the two disagreed by 0.8 or more, the programme took the value the record gives that rank, which keeps the spread of the scale. It is the part of the record most open to disagreement.

Works and people

The paradigms carry their landmark works – 149 papers, 84 books, 17 events and 2 pieces of software, 252 in all – and 629 people, each with a note on their part in a paradigm; the 42 who worked in three or more paradigms have a short biography. The reading panel lists both.

The influences

An influence runs from a source paradigm to a target. It is one of five kinds. The kinds are tested in this order, and the first that fits is used:

• Critique (17): the target defines itself partly against the source, as Haraway’s sympoiesis answers autopoiesis.
• Evolution (14): the target grows out of the source’s own community, whose people or institutions carry the work on under new questions.
• Synthesis (19): the target unifies several programmes into one framework and names the source among them, or an umbrella programme takes the source in as one of its parts.
• Application (42): the target takes the source’s methods, models or concepts into its own field and uses them largely as they are.
• Foundation (110): the target builds a theory of its own on the source’s ideas or results, and reworks them on the way.

An influence’s strength, from 0 to 10, rates how much of the target depends on the source; on the map it runs from 4 to 9. An influence is included when a citation, an acknowledgement or a historical account documents it. Where the only evidence is shared people or concepts, it is rated 5 or less, or left out. Strength is an editorial judgement from the sources. It has been checked against how often each target’s literature cites the source’s key works. That check confirms the strongest influences. It cannot rank the middle of the scale, judge influences before 1980, when the literature database is thin, or tell a critique from agreement.

An influence’s year is its earliest documented transmission: the paper, book, talk, course or institution through which the source’s ideas took hold in the target. The reading panel names that work. A transmission can come before the target began.

No paradigm takes more than seven sources. Where ideas cross-pollinated, influences may run both ways between two paradigms or close a loop, when they are strong or carried by a dated work or event, and never as a critique. Influences that are weak, rest on a single passing citation or break these rules are recorded with their reasons and left off the map.

Uptake and generativity

Two indices measure each programme year by year. They are kept apart because they answer different questions.

• Uptake is cultural influence: how much the wider literature uses a programme’s name, draws on its founding works and writes about it in books.
• Generativity is scientific progress: how much new work of note the programme itself produces, judged by whether its core work still counts among the most cited in its field and by when its key works appeared. This stands in for Lakatos’s idea of a progressive programme – one that keeps producing new results. His own test, novel prediction, is not measured.

A programme can be widely used long after its new work has thinned. System dynamics kept three fifths of its peak uptake in 2024, while its generativity stood at a fifth of its peak. Generativity is the leading measure: it dates the lifecycle.

The data

Publications are the works in OpenAlex whose title or abstract matches a search query written for the programme. The query joins the programme’s name with a few distinctive phrases and shuts out namesakes; generic phrases such as “complex systems” count only together with a second term. The query for Catastrophe Theory, for example, matches “catastrophe theory” and the named catastrophes, such as the cusp, but shuts out “error catastrophe”, a theory of ageing. Where two queries overlapped by construction, the shared works go to the programme whose subject they are: complex adaptive systems in organisations, leadership and health care count for Complexity & Organisation, not for Complex Adaptive Systems. Works in the most cited tenth of their year and subfield count ten times as much. That tenth is taken among the subfield’s articles that carry a reference list in OpenAlex. OpenAlex’s own flag ranks a work among all the subfield’s items, and in subfields where most are never cited, such as cultural studies, one or two citations pass it. Before about 1990 few articles carry a reference list. Where a subfield has too few in a year, the bar comes from its field, or from all its articles, each scaled by the subfield’s own ratio to it in 1990–2005. A book chapter or conference paper is measured against works of its own type, whose bar lies at about a quarter of the articles’. A work in another language than English is measured against the articles in its own language, so that a German school is not judged by the citations of English journals. A canon work counts once, in the canon. Each query is checked by hand:

• Precision – the share of matches that are really about the programme. Random samples from three eras are read and judged; weak queries are rewritten and judged again.
• Recall – the share of the programme’s key works that the query finds. It is often low, because founding works often come before their field’s vocabulary: Lorenz’s “Deterministic Nonperiodic Flow” never says chaos.
• Core or application – samples of the most cited matches are sorted into core work (developing the programme’s theory, methods or self-understanding), applications to another field’s question, and off-topic matches.
• The early tail – many early matches are misdated or off-topic. So the works matched before a programme’s start and in its first ten years are judged one by one, or in samples where there are many. For four programmes whose start has since moved later – chaos theory, phase transitions, catastrophe theory and cellular automata – the first ten years were counted from the earlier start. The judgements correct only the years they cover; the rest of the decade takes the era’s samples. All but three matches before a programme’s start, from 1925 on, are judged. Of these 891 works, 616 are false matches and 249 precursors; both are taken out of the counts. The few precursors the programme’s own works cite join its ancestors. The other 26 are the programme’s own work or applications, and stay in.

Canon uptake counts the works that cite the programme’s key works – its canon – whatever words they use. A paper that builds on Prigogine without saying “self-organisation” still counts; this makes up for low recall and for a field’s words drifting over its life. Books are how often a few defining phrases appear in the English Google Books Ngram corpus. Institutions and events are dedicated institutes, journals, societies, conferences and degree programmes, each with its years checked on a cited source.

From counts to indices

Each correction answers one distortion in the raw counts.

Home-field size

Publications are divided by the size of the programme’s fields that year, because fields differ hugely in size.

Growth of the literature

Citing works are counted per million works published that year, so recent decades do not dwarf the 1950s by volume alone.

Length of reference lists

Citing works are divided by the average length of reference lists, because longer lists alone raise the count.

Abstract coverage

Matches found only in an abstract are divided by the share of the programme’s own title matches that have an abstract that year, relative to 2000–2020, because OpenAlex has abstracts for far more recent works than old ones. Where a year has few title matches, that share leans on the common curve of all programmes.

Precision

Counts are multiplied by the share judged relevant, because false matches are common in some eras and rare in others.

Early-tail noise

The years judged in the early tail use their own judgements, because their matches are far noisier than later ones. Matches before a programme’s start that are false matches or precursors are left out altogether.

Canon cap

No key work may hold more than a quarter of a programme’s citations, so one famous paper cannot drive its curve.

Common scale

Each indicator is divided by its average over a period where all are reliable, so works, citations and book counts can be averaged. The averages are fixed constants, taken once over the 50 programmes the map held on 22 October 2026, and so is the common curve of abstract coverage: adding or removing a programme changes no other programme’s curves or dates.

Reliability by period

Early publications and citations count less, least before 1955 and fully only from 1985, because OpenAlex is thin before then. Books drop out after 2022, where the book corpus ends.

Smoothing

The series are smoothed over several years, because yearly counts are noisy; a date read off them is good to a few years.

The last years

The series stop at 2024, because later counts are incomplete.

Uptake is then a weighted average of publications, canon uptake and books on the common scale. Events and institutions multiply it by at most one and a half: they never create uptake where there is none, because institutions outlive their programme’s productive years. Generativity has two parts: a programme’s most cited works, counting only the share judged core, since applications are uptake (0.7), and the years in which its canon’s works appeared (0.3). Both parts are on the common scale, so the weight of the canon years against the most cited works is a fixed constant, set by that reference set of 50 programmes, not by whichever programmes are on the map. Every programme but one has 8 to 17 canon works from its own years, whatever its size, so for them the canon years are a term of about the same size. Ecological Economics has 4, because three of its founding books, from 1971 to 1987, are older than the programme. Some programmes have few core works among their most cited: small ones, and large ones whose most cited works are mostly applications. For them the canon years make up most of generativity, and the curve shows mainly when their key works appeared. For 35 of the 50 programmes, the canon years give more than half of generativity at its highest value. That is why the end is read from the most cited core works alone, without the canon years.

The lifecycle

The measurements give each programme a lifecycle in dated stages. Emergence and peak are read off its generativity, compared with the programme’s own highest value, and decline off its most cited core works alone (Start, peak and end, above); the others come from the record.

How the views draw it

The reading panel is the same in every view: a paradigm’s description, years, people, ideas, works and influences; an influence’s kind, strength and the work that dates it; or a person’s part in each paradigm, with a short biography for the people in three or more.

River

The river draws the 50 research programmes from the measurements, without the disciplines. In both readings a band grows with the programme’s uptake. Band heights level off at both ends, so the largest programmes do not overwhelm the rest, and every band stays thick enough to carry its name. In shape and shade, a band is darker the nearer the programme is to its own generative peak, so a small programme at its peak looks as vigorous as a large one. In core and halo, the pale halo is the same band, and the solid core inside it shows how much of the work on the programme is new core work of note: the core’s share of the halo is the share of core works among the most cited in their field in all works on the programme, as on the Lifecycles works scale, drawn in proportion so that a share of a quarter or more fills the halo. A programme whose work is mostly use and application has a thin core. A thread leads into a band from its ancestors. Works and events sit inside their band at their year: on the centre line in core and halo, and in shape and shade off it, towards the programmes they also shaped. The river draws the influences of strength 6 and up as strands; the weaker ones are listed in the reading panel.

Network

Each programme is a sphere sized by its significance, and each influence a link that narrows from source to target. Under Show, the disciplines can be added, each a transparent balloon around a small core, which brings in all 202 influences, and the people, drawn beside the paradigms they worked in.

Lifecycles

The Lifecycles view gives each of the 50 research programmes a panel of its own, on one time axis from 1925 to 2024, the last year measured. The solid line is uptake, the dashed line generativity; the shaded band is the peak stated in the data, and ticks below the baseline mark the programme’s first and last years, so the record can be read against the measurement. Selecting a programme outlines its panel where it stands and marks its works and events below its baseline at their years. The panels start in one column per category, ordered by first year; the tools above the map group them by decade or not at all and sort them by either peak, by the uptake kept today or by name. Grouped, they can be fitted into one column per group, one row per group or lines; in rows or columns every panel has one width, so the years line up from row to row and down each column.

The lines can be read on two scales. Relative to peak, the default, draws each line against its own highest value up to 2024. Every programme fills its panel, which shows the shape and timing of its life – when it emerged, peaked and declined, and whether its uptake outlasted its generativity – but not its size. Works per million in its fields draws counts instead: the solid line the works matched to the programme, less the share judged false matches, the dashed line those among the most cited tenth that are judged core, both per million works of the programme’s home fields. These are the publications behind the two indices, without citations, books, events or canon years. Both lines share one axis, whose top value the panel prints, so it shows how large a programme’s literature is and how much of it is top-decile core work. The axis has a square-root scale, so small values are not lost at the baseline. It is labelled at its top and at a quarter of its height, which is a sixteenth of the top value. In the median programme, top core works peak at a twentieth of all works’ peak, which the square root draws at just under a quarter of the height. The home fields differ in size, so heights compared across programmes are indicative.

Two limits matter for reading it. The indices are smoothed over nine years, four on either side, and most of their parts over five years before that. On the works scale the counts are smoothed once, over nine years. So a rise or a fall is spread out, and a date read off a line is good to a few years. They stop at 2024: a line that ends high may still be rising or already falling.

In the network view, the Show menu can hide each kind of influence. The river needs Chrome 111, Edge 111, Safari 16.2, Firefox 113 or a later version, for its colours; the network view needs WebGL.

Limits

• OpenAlex is thin before the 1960s. The early decades rest more on books, key works and events than on publications.
• The literature counted is mostly English; only Morin’s general complexity is searched in French, Spanish and Portuguese as well. Some key works, such as Bogdanov’s Tectology, could not be found in OpenAlex.
• The line between core work and application is a judgement, and two rounds of judging do not always agree.
• Small programmes – Complexity Sociology, Basal Cognition and Cynefin, with 135 to 355 matched works each since their start – are measured noisily, so the strengths of the influences into them rest mostly on the literature.
• Umbrella programmes score low in generativity. Complexity science’s own science is counted under its offshoots, such as network science.
• Institutions are shared among programmes in fixed proportions, though several moved from one programme to another.
• Histories of the sciences under-credit women and others outside the field’s centres. We actively try to correct for this bias, but omissions surely remain.

Sources

Dates and influences rest on primary works and their reference lists wherever these could be read, on historical accounts (such as Waldrop’s Complexity) and, for founding dates, on the Wikipedia articles of each field. The measurements rest on OpenAlex, the Google Books Ngram corpus and the pages of the institutions themselves. The data files carry the work behind every influence and can be downloaded: paradigms, influences, descriptions, people, works and the measured uptake and generativity.

Contributions

The map was researched and built using Claude, Anthropic’s AI model. I directed research and development, defined the information architecture and conceptual framework, and made all editorial decisions. Claude searched and read sources, drafted the data and the descriptions, wrote the OpenAlex queries and judged the sampled works under written rubrics, each verdict with its reason. Claude also wrote the code; I tested, reviewed and edited. Claims were checked against publicly available sources where possible. Linda Doyle contributed important feedback and great ideas – the network view wouldn’t exist without her.

All descriptions should be considered drafts under review. Errors are likely in a map of this size; corrections are most welcome.

Licences

The data – paradigms, influences and descriptions – is in the public domain under CC0 1.0; attribution is welcome. The design and code are published under Creative Commons Attribution-ShareAlike 4.0. The typefaces (Literata, Archivo) are under the SIL Open Font License; d3 and three.js under the ISC and MIT licences.