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Emergent three-dimensional domed stromatolite surface produced by the circular domed growth model
Welcome to the *Stromatolite Growth Modelling- project.
This project explores how some of Earth’s earliest complex biological structures can be reproduced using relatively simple computational models.
Rather than attempting to simulate every microscopic process occurring within a microbial mat, the project focuses on the larger ecological interactions that govern stromatolite development: microbial growth, sediment deposition, burial, photosynthesis and changing environmental conditions.
The aim is to investigate how these interacting processes can give rise to the layered structures preserved in the fossil record.
By deliberately separating biological processes from spatial representation, the project demonstrates how increasingly realistic stromatolite morphology can emerge without requiring increasingly complicated biology.
Beginning with a one-dimensional reference implementation and progressing through increasingly sophisticated spatial representations, the project demonstrates that the same underlying biological model can reproduce a fully three-dimensional domed stromatolite simply through successive refinements of geometry. This progressive approach provides a transparent link between biological assumptions, computational implementation and the complex morphologies preserved in the geological record.
Stromatolites are among the oldest large-scale biological structures on Earth, with a fossil record extending back more than three billion years.
They provide an extraordinary record of the interaction between life and environment during the early history of our planet.
Although their internal structure can appear remarkably complex, many of the processes responsible for their formation are conceptually simple. This makes stromatolites an ideal subject for computational exploration.
The question underlying this project is straightforward:
Can realistic stromatolite growth emerge from a relatively small set of biologically meaningful mathematical rules?
This project is intended as an exploration rather than a definitive scientific model.
Where possible, the implementation favours:
- Biologically interpretable equations
- Modular environmental processes
- Transparent mathematical assumptions
- Computational simplicity
- Incremental model development
Many visible features are deliberately allowed to emerge—and now demonstrably do emerge—from the interaction of relatively simple ecological processes rather than being explicitly prescribed.
As the project evolves, new mechanisms are added only where they improve the biological realism or explanatory power of the model.
The project consists of a common biological framework implemented across progressively richer spatial representations and increasingly realistic stromatolite geometries.
Each successive implementation preserves the same governing biological equations while extending only the spatial representation, demonstrating how increasingly realistic stromatolite morphology can emerge without increasing biological complexity.
- The one-dimensional model provides a reference implementation of the governing biology
- The two-dimensional model extends these equations into a spatial cross-section
- The three-dimensional rectangular model establishes the complete three-dimensional computational framework
- The circular masked model applies that framework to a realistic stromatolite footprint
- The circular domed model introduces realistic stromatolite morphology while preserving the existing biological model
Throughout each stage, the biological equations describing microbial growth, sediment accumulation, photosynthesis and burial remain unchanged while the geometric representation becomes increasingly realistic.
The biological processes are described by a set of coupled growth equations representing interactions between:
- Microbial growth
- Photosynthetic activity
- Sediment accumulation
- Burial
These continuous processes are integrated numerically through time.
The current implementation extends the core equations with an event-driven layered model.
As the simulation progresses:
- The uppermost microbial mat grows continuously
- Sediment is deposited onto the living surface
- Burial events terminate growth of the active layer
- A new microbial mat is established on the newly buried surface
- Older buried layers remain preserved within the developing stromatolite
This combination of continuous growth and discrete ecological events allows the characteristic laminated structure of stromatolites to emerge naturally from repeated cycles of growth, burial and recolonisation.
Environmental conditions are represented as independent forcing functions that modify the biological growth rates without changing the underlying biological framework.
Current forcing includes:
- Seasonal light variation
- Annual temperature cycles
- Light attenuation through the overlying water column
- Sediment-driven burial events
Each forcing function represents a distinct environmental process and can be enabled, modified or extended independently, allowing increasingly realistic ecological scenarios to be explored while maintaining a transparent and modular model architecture.
The project currently contains several complementary implementations of the core biological model.
The one-dimensional model represents a single vertical growth column and serves as the reference implementation of the biological equations.
It provides a transparent framework for understanding microbial growth, sediment burial and lamina formation before introducing spatial complexity.
The two-dimensional model extends the same biological framework across a horizontal transect composed of many interacting growth columns.
Each surface location evolves according to the same governing equations while responding to its own local environmental conditions, allowing spatial variability and evolving surface morphology to emerge naturally.
The three-dimensional rectangular model extends the same biological framework across a complete two-dimensional microbial surface. Each surface location evolves independently according to the core biological model, allowing gentle three-dimensional morphology and internal laminated structure to emerge naturally from local environmental history. This implementation provides the computational foundation for future domed and circular stromatolite models.
The circular masked model applies the existing three-dimensional biological framework to a circular growth domain more representative of natural stromatolites.
No new biological processes are introduced. Instead, growth is confined to a circular microbial colony, demonstrating how realistic colony geometry can emerge simply by changing the spatial representation while preserving the underlying biological model.
The circular domed model extends the circular growth domain by introducing an idealised domed stromatolite geometry representative of many natural stromatolites.
The underlying biological model remains unchanged. Instead, a configurable domed surface provides the geometric framework upon which microbial growth, sediment accumulation and burial processes act throughout the simulation.
This implementation demonstrates how recognisable stromatolite morphology can emerge through geometric refinement alone, completing the progression from one-dimensional biological growth to a fully three-dimensional domed stromatolite.
The pages in this Wiki fall into three complementary categories:
- Core biological processes describe the governing equations and ecological mechanisms underlying stromatolite growth
- Computational implementations describe how those biological processes are represented within the different spatial models
- Model interpretation explains how to read and interpret the diagnostic outputs produced by each implementation
This organisation reflects the philosophy of the project: the biological model remains constant while progressively richer spatial representations are explored.
The project aims to:
- Explore the mathematics of stromatolite growth
- Investigate the interaction between biology and environment
- Develop an interpretable computational model
- Generate realistic layered structures through emergent behaviour
- Investigate how biologically meaningful three-dimensional stromatolite morphology emerges from simple ecological interactions operating within progressively more realistic spatial geometries
- Provide an accessible explanation of the underlying mathematics
Equally importantly, the project serves as a computational natural history exercise, demonstrating how relatively simple mathematical models can illuminate biological processes operating over geological timescales.
The project has been developed as a sequence of deliberately incremental steps. Rather than increasing both biological and computational complexity simultaneously, each implementation introduces only one major conceptual advance while preserving everything established previously.
This approach allows every stage to be understood, tested and evaluated before moving on to the next:
- One-Dimensional Reference Model — establish and validate the core biological growth model
- Two-Dimensional Cross-Section Model — demonstrate that the same biology scales naturally across a spatial surface
- Three-Dimensional Rectangular Model — extend the computational framework into fully three-dimensional space
- Three-Dimensional Circular Model — remove the artificial rectangular boundary while preserving the same biological model
- Three-Dimensional Domed Model — replace the idealised flat surface with a biologically plausible stromatolite morphology, again without changing the underlying biology
- Future Development — investigate emergent dome formation, expanding microbial colonies, erosion and increasingly realistic environmental interactions
The progression is therefore not simply a sequence of increasingly sophisticated geometries. Each stage answers a specific modelling question while demonstrating that increasingly realistic stromatolite morphology can emerge from the same underlying biological principles. This incremental philosophy keeps the relationship between biological assumptions, computational implementation and observed morphology both transparent and scientifically interpretable.
The interactive visualisation developed alongside the domed model extends this philosophy into scientific communication: it changes how the results are explored, not the science that produces them.