Consider how science works. A researcher observes something unexpected — a disturbance. She gathers data, reads prior work, forms a preliminary picture. Then she commits to a hypothesis. She builds an experiment, tests it, discards what fails, selects what survives. She publishes — the work encounters the world. Other researchers replicate, challenge, extend. If the finding holds, it becomes established knowledge: maintained, defended, gradually refined.
That sequence — perturbation, construction, encounter, conservation — is the same sequence a star follows from gas cloud to main sequence. The same sequence a cell follows from signal to division. The same sequence a tumour follows from mutation to metastasis. It is the path every dissipative system takes when it maintains itself by spending energy.
The scientific method is itself a dissipative process. The hypothesis lives in the Construction regime — built under constraint, tested, some fail, one is selected. Peer review is Encounter — what was built meets the world. Textbook knowledge is Conservation — maintained by the field until the next perturbation displaces it. The method runs the geometry it was looking for.
Generative Geometry is the structural science underneath the domains. It does not replace physics or biology or ecology. It identifies the geometry that all dissipative processes share — the sequence, the regime transitions, the fractal depth — and derives it from two operations and nothing else. The formula above is the same formula that predicts drug combination response rates in oncology. It is not an analogy. It is one geometry, expressed in different materials.
Everything that maintains itself — a star, a cell, a company, a habit — does so by running two operations over and over.
Hold keeps things together. It is the force of coherence — what prevents a system from flying apart. Gravity holds a star together. A cell membrane holds a cell together. A shared mission holds a team together.
Cross enables exchange. It is the force of transformation — what allows the system to interact with what is outside it. Nuclear fusion transforms hydrogen into helium. Metabolism transforms food into energy. A product launch transforms an idea into a business.
Each operation is either latent (present but not yet engaged) or active (fully engaged). Two operations × two states = four possible combinations. These four combinations always occur in the same order. They form a cycle. Every dissipative system in every domain runs this cycle.
At each transition, one operation changes state. The labels at the arrows tell you what is ending and what is beginning — because at every threshold, both happen in the same breath.
Each regime contains four steps. The same two-operation logic that creates four regimes from one cycle also creates four positions within each regime — and four sub-positions within each position. The structure repeats at every scale. This is why a star forming, a cell dividing, and a company growing all pass through the same sequence: not because they are metaphorically similar, but because they are running the same structural geometry at different scales.
Click any position to see the same step in three different systems.
Explore the geometry. Run the calculations. Verify the predictions. Every tool computes from first principles — two operations, integers, and π.
Generative Geometry was developed by Raimo van der Klein over twenty-five years of observing change in teams, organisations, and systems. The pattern was discovered empirically, formalised structurally, and tested quantitatively across seven scientific domains.
Van der Klein is COO of Pacmed (AI-powered hospital capacity management) and co-founder of Layar (world's first mobile AR browser, 40M+ users). The book Riding Change: How Change Moves, and How to Move With It presents the framework for a general audience.
This is an independent research programme. It is not affiliated with any university or institution. The work is published open-access and the tools are freely available. The geometry belongs to everyone who studies it.