Algorithmic Design In Watchmaking And Jewelry.

Sections In This Article

• What Is An Algorithm?
• What Is Algorithmic Design?
• Fractals Are Generated By Algorithms
• How Nature Uses Algorithms
• Uses Of Algorithms In Art And Design
  • Visual arts
  • Music and Sound Design
  • Architecture
  • Other Areas Of Art And Design
• Algorithmic Design In Jewellery
• Algorithmic Design In Watchmaking

Introduction

This article focuses on how algorithms are used to produce the results of a design process. This is a different, although related, topic to “algorithm design” which means how algorithms themselves are designed.

For example, in this article I will show you how free software allows you to guide an algorithm to produce a specific type of beautiful images, which would be a use of algorithmic design.

On the other hand, a human designing an algorithm which then becomes part of a larger software system, would be an example of algorithm design, which we’re not looking at in this article. Just to mention though, because it is conceptually interesting, algorithms can now design algorithms . . . an employee of one of the big social media platforms asked ChatGPT to create the new ideas he should have created himself that week for the platform, and to write the code (algorithms) to implement them, and the AI wrote original code which worked correctly!

Why am I talking about algorithmic design in jewellery and watchmaking together? The two industries have been closely linked from early in the evolution of watches, and still have a strong symbiotic relationship rooted in precision craftsmanship and artistic expression. Both fields encompass intricate detailing, precise engineering, and a commitment to desirable aesthetics. Watchmaking often incorporates elements of jewellery design in its cases, dials, and adornments, while jewellery design draws inspiration from watchmaking’s precision mechanisms, materials, and design intricacies. Their shared craftsmanship, attention to detail, and pursuit of timeless elegance bridge the worlds of adornment and timekeeping, creating a harmonious synergy between these two disciplines.

There are even direct links, such as Swiss jewellers having to become watchmakers due to the prohibition of jewellery in 1541, which can be said to be the birth of the Swiss watchmaking industry.

Our own watches (below) could be considered to be more about jewellery aspects than watchmaking or time-telling aspects (although not the usual fine jewellery that people are most familiar with). Also, algorithmic design applies in similar ways to both watchmaking and jewellery design, as I’ll detail below.

As is usual in my blog posts, I’ll be including some relatively well-known perspectives on these topics, but also delving a little deeper, into little-known and sometimes controversial areas.

Note . . . I only use images with permission from the watchmaker (unless the photos are public domain or creative commons), so some of the examples I present here might be lacking an image.

What Is An Algorithm?

An algorithm is a precise set of instructions or rules designed to produce a specific results, such as to solve a problem, perform a task, or accomplish a specific objective.

Algorithms are a fundamental part of computer science and are used extensively in various fields, including mathematics, engineering, data science, and artificial intelligence.

Key characteristics of algorithms include clarity, precision, and effectiveness. A well-designed algorithm should be clear and unambiguous, allowing anyone familiar with the problem domain to understand and follow the steps. Precision ensures that each step is precisely defined without ambiguity or vagueness. Effectiveness refers to an algorithm’s ability to solve a problem efficiently within a reasonable amount of time and using a manageable amount of resources, such as memory or processing power.

Algorithms serve as the backbone of computation, powering the technology and systems that define our modern world. From simple everyday tasks to complex computations in cutting-edge technologies, algorithms play a pivotal role in solving problems and driving innovation.

What Is Algorithmic Design?

Algorithmic design refers to the process of using algorithms to produce specific types of results in various fields.

A simple example is a Spirograph, a children’s toy which uses a system of cogs with holes for pens, to create attractive geometric shapes. The ratio between the sizes of the cogs, and the position of the holes for the pens, form an algorithm, encoded in the physical parts, to produce visual designs:

The process of algorithmic design often begins by thoroughly comprehending the problem at hand, breaking it down into smaller, more manageable components. This step involves analysing the problem’s requirements, constraints, and desired outcomes. It’s crucial to have a clear understanding of the problem and the context in which the solution will be applied.

Following problem analysis, algorithmic design involves devising a way to use an algorithm to generate desired results. The degree to which this is an experimental process can vary widely. Sometimes the desired result is known with a fair degree of accuracy before the algorithm is used, sometimes the algorithm is chosen so as to produce unexpected results, then usually modified or redefined by the human user.

For example, AI (which is algorithms) can be used to generate new and somewhat unpredictable results, then the Prompts used can be refined or extended to generate results which the user finds more interesting. Those results might be used directly, further developed, or used as starting-point ideas for human design projects, as some watchmakers have done (see below).

There are many artists who use mathematics. The results are sometimes very predictable and chosen beforehand, other times very much an exploratory process of observations guiding further experimentation, sometimes producing results far from what was envisaged at the start. Use of fractals often falls into the latter category, especially as they are fundamentally chaotic in nature, with small changes in parameters sometimes producing major differences in output.

Increased use of algorithmic design, often generating more complex results than ever before (as with fractal art, below), aligns with the change in the Western Art Tradition from simple concepts such as the simple geometric shapes used in fine jewellery, to the much more complex forms and surfaces used in art jewellery, such as organic or fractal elements.

Fractals Are Generated By Algorithms

All fractals are generated by algorithms. This applies whether they are generated by humans or by nature (see below), because a natural system uses a precise set of rules to generate their outcomes, even if we don’t yet understand exactly how those rules are encoded by genetic data or other systems.

While it is theoretically possible to create some types of fractal patterns manually, it is unrealistic to do so. So fractals were only discovered (in the 1970’s, by Benoit Mandelbrot) when computers were able to rapidly and correctly repeat simple instructions a very large number of times.

Fractals, known for their self-similar and infinitely detailed patterns, are generated by algorithms using iterative processes. Algorithms for fractal generation rely on repeating often relatively simple mathematical calculations that produce complex patterns near the boundary between chaos and order, by applying a set of rules recursively.

There is an easy way to explore algorithmic design yourself, for free, using GIMP:

So that was an example of a two dimensional fractal. I’ve seen animated flame fractals used in the background environment of science fiction movies. Other types of fractals are commonly used to generate the surfaces of planets and other elements of movies, especially in the science fiction genre.

Fractal art is also a significant genre, still evolving as new possibilities open up, such as . . .

Some fractals can have three or more dimensions:

I’ll show you a fascinating example of a use of a three (actually four) dimensional fractal in watch creation, below.

How Nature Uses Algorithms

The algorithmic nature of how the natural world, whether in living, or non-living systems, is very evident in the results, whether we’ve discovered how those physical algorithms work, or not, since the definition of an algorithm is a precise set of instructions or rules designed to produce a specific results.

Most of the algorithms used in nature are fractals. Examples include:

Growth patterns seen in plants and trees are mostly fractal, such as the branching structures of trees or the arrangement of leaves.

These patterns usually follow algorithmic rules, like the Fibonacci sequence, resulting in efficient use of space and resources while maximizing exposure to sunlight for photosynthesis.

Another example of nature employing algorithms is found in the foraging behaviour of many animals. Creatures like bees, ants, and birds utilize optimized search algorithms when foraging for food. For instance, ants use a method called “ant colony optimization,” where individual ants leave pheromone trails, allowing others to follow the most efficient path to the best food sources. This collective behaviour is an algorithmic process (because it is based on rules which can be deduced), enabling the entire colony to find the shortest path to food.

Animals’ movement patterns, such as the flight of birds in flocks or the movements of fish in schools, demonstrate algorithms governing group behaviour for efficient navigation and predator evasion. These collective behaviours involve simple rules such as maintaining distance from other members within specific limits, which, when implemented by large numbers of members also reacting to environmental factors, result in complex and beautiful patterns:

From the way proteins fold to the migration patterns of animals, nature’s algorithms offer valuable insights for problem-solving, optimization, and adaptive strategies, inspiring advancements in various fields, including artificial intelligence, optimization algorithms, and problem-solving methodologies, which are often the basis of man-made technologies.

Uses Of Algorithms In Art And Design

Algorithms are used in two main ways in art and design:

Firstly there are functional uses, such as increasing manufacturing efficiency, or, in conjunction with 3D printing to increase speed and decrease costs of prototyping.

The second use of algorithmic design is for aesthetics. Algorithms are used in creative fields, generating art, music, and literature. Generative adversarial networks (GANs) create art and deep learning models generate music compositions or assist in creative writing, showcasing how algorithms contribute to creative endeavours.

Algorithms play an increasingly significant role in various design disciplines, revolutionizing creative processes and offering innovative solutions. Their application extends across diverse fields like graphic design, sound design, product design, and more, enhancing efficiency, creativity, and functionality.

Visual arts:

Graphic Design: Generative design algorithms, like those used in Adobe Illustrator’s pattern generation or in data visualization tools, enable the creation of complex designs based on parameters or datasets.

Generative Art: Artists use algorithms to create generative art, where complex and often unpredictable artworks are generated based on predefined rules or algorithms. These rules could involve mathematical formulas, random processes, or data inputs. Generative art produces visually stunning and unique pieces, showcasing the interplay between code, randomness, and artistic vision.

The main starting points for generative art were mechanical and analogue devices in the 1950’s, then digital computing in the 1960’s from artists like Frieder Nake and Herbert Franke. Another example was Vera Molnár who was creating algorithmic drawings in the ’60’s.

Manfred Mohr was using a computer controller plotter to produce drawings relating to his own strong attitudes regarding rhythm and repetition:

From these beginnings, generative art has progressing all the way to AI generated art:

Algorithmic Drawing and Painting: Algorithms assist artists in creating intricate drawings or paintings by automating certain aspects of the creative process. Algorithms can control brush strokes, colour selection, or shapes, enabling artists to rapidly and easily explore new techniques and styles while maintaining a level of control over the final output.

Data Visualization: Visual artists use algorithms to transform complex datasets into visually comprehensible and aesthetically pleasing representations. Through data visualization algorithms, artists depict information using charts, graphs, or interactive installations, allowing viewers to grasp complex information intuitively, resulting in images which are both functional and often beautiful too.

Interactive Art and Installations: Algorithmic design facilitates interactive artworks that respond to audience input or environmental stimuli. Artists create immersive installations or experiences using sensors and algorithms to generate real-time visual outputs, fostering dynamic interactions between the artwork and the viewer.

Computer Graphics and Animation: Algorithms underpin computer graphics and animation, enabling artists to create realistic simulations, special effects, and animations in movies, video games, and virtual reality. Rendering algorithms simulate light, textures, and motion, bringing imaginative worlds to life.

One of the milestones in CGI (computer generated imagery) was the movie “Jurassic park” which was made using SoftImage software:

I also happened to be part of the team at Stainless Software, in 1997, who, with their acclaimed Carmageddon (#1 game in the world, that year) released the first computer game based on real physics (we had a PhD physicist working with us) . . . if you turned the steering wheel and held the hand-brake on, you got a realistic hand-brake turn, and you could use deliberately placed wedge-shaped objects to jump the car over other objects etc. all done with algorithms modelling the moments used in physics to calculate how cars interact with their environments.

In my own view, a later significant milestone in computer graphics was “Avatar”, where I found myself engrossed in the beauty of the world, without considering that it was computer generated.

It could also be said that the many movies where most people have no idea CGI has been used at all, are a testament to the realism of what today’s software can create.

Music and Sound Design:

In audio creation, algorithms aid in sound synthesis, digital signal processing, and music composition. Synthesizers use algorithms to generate various sounds by manipulating waveforms or modelling physical instruments. Digital audio effects (reverb, equalization, auto-tune etc.) rely on algorithms to modify audio signals in real-time.

Algorithmic Composition: Musicians and composers use algorithms to generate musical compositions based on predefined rules or parameters. These algorithms can employ mathematical models, random processes, or AI-driven approaches to create melodies, harmonies, rhythms, or entire musical structures. Algorithmic composition offers novel ways to explore musical ideas, genres, and styles.

A very simple example of algorithmic composition I created myself when studying music in university around 1990. We were asked to create a piece of music using random notes. I was unsure which method I wanted to use for the random notes, so used several, one involving using a random number generator on a computer to determine the pitch and length of each note. I also created part of the composition by writing what I thought would sound random, and left another section to be improvised live.

Digital Sound Synthesis: Algorithms are employed in sound synthesis techniques like granular synthesis, FM synthesis, and physical modelling synthesis utilize algorithms to generate diverse sounds, textures, and timbres.

Interactive Installations and Sonic Art: Algorithmic design facilitates interactive sonic art installations that respond to environmental stimuli or audience interactions. Sensors, algorithms, and generative processes create immersive and dynamic sonic experiences in art installations or interactive exhibits.

Architecture

Algorithmic design has profoundly influenced the field of architecture, revolutionizing the way architects conceive, design, and construct buildings. It empowers architects to optimize designs, generate complex forms, analyse environmental factors, and streamline the architectural process.

Parametric Design: Architects use parametric design tools and algorithms to create designs based on defined parameters and rules. These tools enable the manipulation of design elements like shapes, patterns, and structures, allowing for adaptive and responsive designs. Parametric design aids in creating intricate and innovative architectural forms that respond to specific criteria or constraints.

Generative Design: Architects utilize generative algorithms to explore numerous design possibilities and generate diverse architectural solutions. These algorithms use iterative processes and computational models to generate and evaluate design alternatives based on specified objectives, optimizing for factors like structural integrity, energy efficiency, or aesthetic appeal.

The Rhino software with the Grasshopper Plugin is used for generative architectural design, such as repeating shapes or patterns of various types including fractals.

Environmental Analysis and Simulation: Algorithms aid architects in analysing environmental factors like sunlight, wind flow, and energy performance. Simulation algorithms model and predict the impact of these factors on buildings, enabling architects to design structures that maximize natural light, ventilation, and energy efficiency.

Structural Optimization and Engineering: Algorithms optimize structural design and engineering by analysing complex loads and stresses on building components. Structural analysis algorithms help architects design efficient and resilient structures while minimizing material usage.

Urban Planning and Landscape Design: Algorithms assist in urban planning by simulating urban growth, analysing traffic patterns, and optimizing spatial layouts. Landscape design benefits from algorithms that generate naturalistic forms or simulate ecological systems to create sustainable landscapes.

Responsive and Interactive Architecture: Algorithmic design facilitates the creation of responsive and interactive architectural elements. Sensors, actuators, and algorithms enable adaptive architecture that responds to changing environmental conditions or user interactions, enhancing functionality and user experience.

Other Areas Of Art And Design

I’ll cover jewellery and watchmaking in separate sections, below, but first, here are a few other areas of art and design which use algorithmic design:

Product Design: Parametric design tools employ algorithms to create designs based on specified parameters, allowing rapid prototyping and iterative design processes.

Industrial Design and Manufacturing: Algorithms optimize manufacturing processes, material selection, and production workflows. Additive manufacturing (3D printing) uses slicing algorithms to convert digital models into printable layers, while optimization algorithms enhance efficiency in production planning and resource allocation.

Fashion Design: Algorithms are applied in fashion design for pattern generation, textile design, and even trend analysis. Pattern-generating algorithms help create intricate designs, while AI-driven algorithms analyse fashion trends, consumer behaviour, and preferences to predict future styles as well as creating new ideas:

Algorithmic Design In Jewelry

Algorithmic design has significantly impacted the realm of jewellery, offering designers innovative tools and methodologies to create intricate, personalized, and avant-garde pieces. By blending technology, creativity, and craftsmanship, algorithmic design revolutionizes traditional jewellery-making processes, enabling designers to craft unique and complex designs that push the boundaries of artistic expression. Here’s how algorithmic design is employed in the field of jewellery:

Parametric Design: Jewellery designers utilize parametric design tools and algorithms to create customizable designs based on specified parameters. These tools enable the manipulation of shapes, patterns, sizes, and textures, allowing for adaptive and personalized designs tailored to individual preferences.

Generative Algorithms: Generative algorithms help jewellery designers explore a multitude of design possibilities by generating diverse and intricate patterns, forms, and structures. By employing iterative processes and computational models, designers can create and evaluate numerous design variations, offering unique and avant-garde jewellery concepts.

Customization and Personalization: Algorithms enable customization and personalization in jewellery design. Designers can create bespoke pieces tailored to specific customer preferences, such as unique engravings, personalized shapes, or custom-fit designs.

Complex Geometries and Patterns: Algorithmic design allows for the relatively easy creation of complex geometries and intricate patterns that were previously challenging or impossible to achieve manually. Geometrically complex shapes, interlocking patterns, and organic forms inspired by nature are made feasible through algorithm-driven design processes.

Digital Fabrication Techniques: Algorithms are integrated into digital fabrication processes such as 3D printing, laser cutting, or CNC machining. Slicing algorithms translate digital designs into printable layers, enabling precise and intricate detailing, intricate textures, and complex structures in jewellery production.

Material Optimization and Efficiency: Algorithms aid in optimizing use of precious materials and minimizing waste in jewellery production. Designers can utilize algorithms to create intricate designs while reducing excess and contributing to sustainability in the jewellery-making process.

Experimental and Artistic Jewellery: Algorithmic design empowers jewellery artists to experiment with unconventional materials, innovative forms, and avant-garde concepts. Artists create artistic jewellery pieces that challenge traditional notions of adornment, often using algorithmic approaches to achieve unique and boundary-pushing designs.

Examples of algorithmic design in jewelry-making.

Folium is a new algorithmic jewellery series by “Nervous System” using algorithmic design based on structures of plants and algae to create unique one-off designs. It uses a multistage digital growth process based on L-systems and spatial colonization algorithms, with the outer shape and the inner structures influencing each other as the design evolves.

Other jewellery designers are using Rhino software with the Grasshopper Plugin for a much quicker and easier way to generate and manipulate complicated and repeating forms. This approach has evolved from being a specialist area for mathematicians and programmers, to now being easy to use, and so popular there is even a dedicated website for generative jewellery design.

UnconstrainedTime has created what is almost certainly the first ever 3D fractal watch. I am putting it here because, although it is a watch (it tells the time), it could be considered to be more about art jewellery design than watch design, since it aligns more with conceptual art jewellery than it does with anything relating to traditional watchmaking.

My background is fine art and cutting-edge contemporary music is part of what led me to create this very unique watch, combining a 3D Julia fractal with the simplest design I could make for the rest of the watch, ensuring the focus is on the beauty and wonder of the fractal itself.

Our fractal emergence watch can certainly be considered an example of experimental and artistic jewellery:

Algorithmic Design In Watchmaking

I showed an example of algorithmic watch design and/or jewellery design, above . . . my Fractal Emergence watch, which is almost certainly the first 3D fractal watch ever created:

Another example of algorithmic watch and/or jewellery design is our Tropical crystal watch. I wanted something similar to the tropical tree roots of the strangler fig, which I find beautiful, fascinating and evocative:

So I asked the 3D designer to start with the donut-shape , then use an algorithm to twine a series of thinner elements around it. The thinner the element, the more times it circled the donut shape.

After several experiments (some of which I have kept for use in later designs), I was happy with the results:

When I came back to the UnconstrainedTime project at a later date, being more realistic about dimensions necessary to incorporate the time-display components, as well as materials for the metal of the watch, I got the new 3D designer to make some changes to the watch design, and render it in materials including bronze and black anodized aluminium:

We’re launching in 2025 with our Fractal Emergence watch, shown above, so . . .

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Humism watches:

. . . by an independent design studio based in Singapore, have kinetic sculptures showing moving mathematical patterns. They say “Inspired by the watch as an artistic medium, we seek to create beauty out of time’s movement.“

A very interesting watch relating to the digital world, is the “Genesis” by H. Moser and Cie:

Each watch includes a unique QR code (which is, of course, designed by an algorithm) engraved inside the sapphire glass, which links to blockchain product authentication created as each watch completes its production, and other exclusive privileges enabled by the VIP keypass giving access to digital assets, redefining the customer experience for the future, including details of the creation of the individual watch. They say “This holistic experience brings together physical, digital, and virtual dimensions.“

The bezel and crown are made from 3D-printed titanium, and features a pixelated aesthetic.

The Bulgari Octo Finissimo Ultra is another example of a watch design with strong links to the digital world. On the top of the mainspring barrel of the watch is a unique QR code, which links to a video and a NFT about that specific watch.

Some designers are using AI, but not to actually design watches. Instead they use it to generate interesting and inspiring ideas to then develop and design by hand. Quotes from designers using AI say that it has no taste, but also say that it is at its beginning, and is likely to evolve hugely in the near future. It has also been said that, once it becomes a lot more usable, AI design is likely to make purely hand designed and hand made watches even more exclusive and expensive than they already are.

The Needle Watch (2017), Designed by Arturo Tedeschi:

. . . using Rhino software with the Grasshopper plugin, was designed by AI, but designed to be inspired by 70’s style watches, and looks like it was designed by humans. So AI doesn’t necessarily have to be aimed at unusual designs. Also, with the current dislike of AI design from some areas, some designers might be using AI but in a way which looks like human design, but improves the design process in some way such as making it quicker or more effective.

As well as in aesthetic creations, algorithms are being used to identify and analyse design options, calculate the best possible materials to use, and create designs for watches which take into account the relevant manufacturing constraints, as well as being applied to optimizations and predictions for marketing.

Here are some of the other ways algorithmic design is employed in watchmaking:

Complex Movement Design: Algorithms play a crucial role in designing and optimizing the intricate movements within watches. The development of movement components like gears, escapements, and balance wheels relies on algorithms for precise calculations and optimization, ensuring accuracy, reliability, and efficiency in timekeeping.

Materials and Structural Optimization: Algorithms aid in optimizing materials and structural designs for enhanced performance and durability. Computational algorithms simulate stress distribution, thermal properties, and structural integrity, assisting in the selection of materials and the creation of lightweight yet robust watch components.

Customization and Personalization: Algorithmic design enables watchmakers to offer much more rapid and cost-effective customization and personalization options to customers. Customized dials, case designs, engravings, or limited editions tailored to individual preferences are made feasible through algorithm-driven design processes.

Prototyping and Rapid Iteration: Digital prototyping and iterative design processes facilitated by algorithms allow watchmakers to rapidly experiment with design variations. This iterative approach aids in refining designs, testing functionalities, and assessing aesthetics before final production, reducing development time and costs.

Precision Manufacturing and Assembly: Algorithms guide precision manufacturing techniques, including CNC machining and laser cutting:

. . . for intricate watch components. Algorithms ensure precise measurements, tolerances, and geometries, contributing to the high precision and quality of watch components during manufacturing and assembly.

Performance Optimization and Accuracy: Computational algorithms assist in optimizing watch movements for accuracy, stability, and performance. Algorithms simulate the behaviour of movements under various conditions, fine-tuning mechanisms, and minimizing friction to enhance precision and longevity.

Horological Innovations and Complications: Complex horological complications, such as tourbillons, perpetual calendars, and moon phases, benefit from algorithmic design. Algorithms aid in the creation and optimization of these intricate mechanisms, ensuring their functionality and reliability.

So . . . what do you think is the most exciting aspect of the future of algorithmic design for watchmaking or jewellery? Comment below or on our social media.