Over millions of years of evolution, living organisms have developed remarkable strategies for optimising the use of resources, maximising energy efficiency and adapting to a variety of environments. Drawing inspiration from these processes, the fields of architecture and urban planning have long been exploring innovative and sustainable solutions to contemporary challenges such as managing urban density, energy efficiency and resilience in the face of climate change.
Algorithms make it possible to mimic these natural dynamics, often through successive iterations when simulating growth processes. These bio-inspired models allow us not only to understand the mechanisms of nature, but also to adapt them to specific needs, whether this means designing lightweight, robust architectural structures or optimising the layout of public areas. Algorithmic processes offer an unprecedented capacity for manipulation and adaptation, paving the way for more fluid, contextual and responsible design. This article explores some of these natural processes, their digital applications and the opportunities they offer in the design of the built environment.
Les fractales : la géométrie infinie de la nature
Fractals, shapes that repeat on different scales, are found everywhere in nature: ferns, tree branches, snowflakes. Using recursive algorithms, we can reproduce fractals such as the famous Mandelbrot set or tree fractals. These systems allow us to study phenomena such as plant growth or the structure of hydrological networks by generating infinitely complex structures from simple rules.
Fractals – Dragon Curve (left) and Voronoï (right) © Datamorphoz
Laser-cut tablet generated with 3 Voronoi iterations © Datamorphoz
Application example
The Grand Egyptian Museum, designed by Irish firm Heneghan Peng Architects, incorporates motifs inspired by fractals, in particular the Sierpinski triangle (described in 1915 by Wacław Sierpiński), into its architectural design. This bio-inspired approach is particularly evident in the Museum’s main façade, where interlocking triangular patterns create a complex and aesthetically compelling structure. It consists of a series of 6 iterations that create a section of the main wall with alternating relief on the triangles. These fractal patterns not only evoke the richness of natural geometry, but also establish a symbolic link with the pyramid shapes emblematic of ancient Egypt. The use of such fractal structures provides visual depth and architectural dynamism, reflecting the harmony between art and science.
View of the Great Egyptian Museum in Cairo © Heneghan Peng Architects
L-systems : le langage des plantes
Created by Aristid Lindenmayer, L-systems are rewriting systems that simulate plant growth. Using iterative rules, these algorithms reproduce the branching of trees, the spirals of flowers or the shapes of certain corals. This method is particularly useful for modelling living organisms and analysing optimal growth strategies in constrained environments.
L-System generated with the Rabbit plugin © Datamorphoz
Application example
A notable example is Michael Hansmeyer’s project ‘L-Systems in Architecture’. In this study, Hansmeyer explores the use of L-systems to create innovative architectural structures. Using these algorithms, he has been able to design complex architectural forms that mimic the natural growth of plants, opening up new possibilities in design and construction.
L-System © Michael Hansmeyer
Cellular automata: complexity generated by simple rules
Cellular automata are mathematical models made up of grids of cells, where each cell can adopt different states and evolve according to local rules depending on the state of its neighbours. This approach makes it possible to simulate complex systems based on simple interactions.
An emblematic example is John Conway’s Game of Life, created in 1970. In this game, each cell in a two-dimensional grid is either alive or dead. At each iteration, the state of each cell is updated according to the following rules:
- A living cell with fewer than two living neighbours dies (sub-population).
- A living cell with two or three living neighbours survives.
- A living cell with more than three living neighbours dies (overpopulation).
- A dead cell with exactly three living neighbours becomes alive (birth).
These simple rules give rise to complex and varied behaviour, illustrating the emergence of self-organising structures.
John Conway’s Game of Life generated by the Rabbit plugin © Datamorphoz
Application example
The cellular automata model can be applied to the generation of non-binary solar envelopes.
In this paper, I explore the development of rule-based algorithmic methods for designing optimised solar envelopes and shapes in an urban context. Shapes are generated from voxels (volumetric pixels) according to rules for access to direct sunlight.
These methods combine computational and environmental tools to design architectural projects adapted to urban constraints. They compare additive and subtractive approaches to generate envelopes and shapes that meet quantitative solar access criteria already used in some countries to ensure lighting and thermal comfort.
“Voxel computational morphogenesis in urban context : proposition and analysis of rules-based generative algorithms considering solar access” @Ilona Pinto de Araujo, 2017
Diffusion Limited Aggregation (DLA) : growth by aggregation
DLA is a process that reproduces patterns formed by the aggregation of randomly moving particles. This phenomenon can be seen in the shapes of ice dendrites, mineral deposits or the roots of certain fungi. In simulation, it gives rise to irregular fractal structures, perfect for understanding how disordered systems can generate coherent and aesthetic patterns.
DLA 2D & 3D © Datamorphoz
Application example
Design studio Nervous System has developed a jewellery collection called Dendrite, directly inspired by the process of Diffusion Limited Aggregation (DLA). This process models the way in which randomly moving particles aggregate to form complex branching structures, similar to crystalline dendrites or coral patterns.
Using algorithms based on DLA, Nervous System generates unique patterns for each piece in the collection. These jewels, precision-cut from stainless steel, reflect the beauty of natural forms resulting from aggregation processes. This approach combines science, art and technology to create objects that capture the organic aesthetic of natural structures.
Pendants from the ‘Full Moon’ series inspired by dentrite © Nervous System
Swarm Behaviour: collective movement and algorithms inspired by swarms
Swarm behaviour can be observed in flocks of birds, schools of fish or groups of insects. This phenomenon is the result of local interactions between individuals following simple rules: separation to avoid collisions, alignment to synchronise with neighbours, and cohesion to stay in the group. These elementary interactions give rise to impressive collective dynamics, often unpredictable but always organised.
Application example
In the digital domain, these models are used to simulate collective flows such as pedestrian movements or crowd management in public spaces. They can be used to better organise places of interaction and optimise traffic flow in train stations, shopping centres or urban parks.
In addition to simulation, swarm behaviour also inspires optimisation algorithms known as colony algorithms (for example, the Particle Swarm Optimisation (PSO) algorithm). Based on similar principles, these algorithms are an alternative to genetic algorithms. Unlike genetic algorithms, which rely on natural selection, swarm-inspired algorithms rely on the exchange of information between agents to quickly converge on optimal solutions. In urban planning, for example, they can be used to optimise the distribution of infrastructure or the energy management of buildings. In architecture, they can be used to generate adaptive forms that respond to structural and environmental constraints.
Reaction-Diffusion : l’émergence des motifs naturels
Reaction-diffusion models, introduced by Alan Turing in 1952, explain the spontaneous formation of natural patterns such as zebra stripes or leopard spots. These mathematical models describe how chemical substances react with each other and diffuse in space, leading to the emergence of regular structures from an initial homogeneous state.
Mesh deformation using a reaction-diffusion model
Focus on the leopard’s coat
The spotted coat of a leopard or cheetah illustrates the reaction-diffusion principles described by Alan Turing in 1952, marking the beginnings of modern theoretical biology. Turing showed that the interaction between two chemical substances (morphogens), one activating pigment production and the other inhibiting it, could generate patterns such as spots or stripes. These patterns are determined by global parameters: the removal of one spot affects the whole, and the shape of the pattern (spots or stripes) depends on the geometry of the system.
For example, the cheetah has spots on its body but stripes on its tail, which is narrower. This can be explained by a geometric transition in the dynamics of the morphogens. Although the Turing mechanism may only act during a brief phase of development, it remains a key model for understanding and predicting animal morphogenesis.
Leopard (Panthera pardus) © Muséum national d’Histoire naturelle
Vascular network system in plant morphogenesis
Vecular morphogenesis is a natural process by which networked structures, such as leaf veins, blood vessels or rivers, emerge. These networks are often formed by optimising the paths between points (for example, to transport nutrients or minimise the energy expended).
The giant leaves of Queen Victoria, a tropical water lily, are famous for their unique structure, consisting of a vast network of veins that support a surface up to 3 metres in diameter. This network is a fascinating example of plant morphogenesis, where the formation of veins is based on natural optimisation processes.
As they grow, these veins form to efficiently transport water and nutrients through the leaf while distributing the mechanical stresses caused by its own weight. This process is guided by the differentiated growth of the cells: areas of high stress or intense water flow stimulate the production of vascular cells, strengthening the stressed areas. This adaptive mechanism follows similar principles to those observed in biological networks such as circulatory systems or roots.
Certain algorithms, such as those based on the venation development method, can be implemented to simulate network formation. These algorithms use starting points (sources) and attractors (resources) to guide the growth of the lines that represent the veins.
Vascular network of a leaf and Voronoi diagram © Datamorphoz
Application example
Optimising urban transport networks is a major challenge for town planners and engineers. One innovative approach is inspired by the structure of leaf veins, which form efficient networks for distributing resources. By analysing the growth process of leaf veins, researchers have developed a bio-inspired algorithm for designing urban transport networks. This algorithm simulates the natural selection and genetic transmission observed in biological evolution, making it possible to generate transport networks that are optimised in terms of connectivity and efficiency. The application of this method to concrete cases, such as the Sioux Falls network, has demonstrated its ability to produce more rational and efficient urban transport solutions.
Source : “Artificial leaf-vein network optimisation algorithm for urban transportation network design” by Baozhen Yao; Chao Chen; Wenxuan Shan; Bin Yu.
International Journal of Bio-Inspired Computation (IJBIC), Vol. 20, No. 4, 2022
Reproducing nature to rethink our spaces
These bioinspired processes, translated into algorithms, offer powerful tools for designing environments that are adapted, sustainable and aesthetically pleasing. In architecture, urban planning and design, they help to solve complex problems while proposing solutions that are in harmony with the ecosystem.