This is an S-curve.

The S-curve is a fundamental pattern that exists in many systems that have positive feedback loops and constraints. The curve speeds up due to the positive feedback loop, then slows down due to the constraints.

When the constraint is broken, the positive feedback loop ramps back up, until it hits another constraint.

Diffusion S-Curves

The S-curve pattern is quite common in the spread of ideas, practices, and technologies, although it rarely looks quite as pretty. The example below shows "diffusion s-curves" - How a technology spreads through a population (in this case US households

The positive feedback loop in this case is word of mouth, and the constraints represent fundamental barriers to certain market segments or growth such as simplicity, usability, scalability, price, etc.

This creates smaller s-curves around adoption among specific market segments, and larger s-curves that represent the overall market penetration of the idea, practice, or technology.

Evolution S-Curves

In addition to Diffusion S-curves in technology, ideas, and practices, there are Evolution S-Curves. These represent the increase in the traits of these ideas that make them usable in more situations and desirable for more people. When you break through a constraint in one of these properties through innovation, this can often coincide with "unlocking" a new diffusion curve by opening up a new market that wouldn't previously have used your technology or idea.

In this case the positive feedback loop is the increased understanding and expertise that comes from diffusion of a new innovation in your idea or technology, and the constraint represents fundamental assumptions in the idea, practice, or technology that must be changed through another innovation to make the idea, practice, or technology more desirable.

In the example below the desirable property is hardware speed. Fundamental leaps are made to break through a speed constraint, and then iterated on through the positive feedback loop of information and expertise increasing from adoption. This hits diminishing returns as the new innovation is optimized, and then a new fundamental innovation is needed to overcome the next constraint.

S-Curves vs. Exponential Growth

Sometimes, people get confused and call S-curves exponential growth. This isn't necessarily wrong but it can confuse their thinking. They forget that constraints exist and think that there will be exponential growth forever. When slowdowns happen, they think that it's the end of the growth - instead of considering that it may simply be another constraint and the start of another S-Curve. Knowledge of Overlapping S-Curves can help you model these situations in a more sophisticated way.

S-Curves Patterns

S-curves become quite useful when paired with an understanding of evolutionary patterns. They can allow you to see in a broad sense what's coming next for an idea, practice or technology. They can prevent surprises and give you a tool to stay ahead of changes.

There are patterns that exist for both diffusion and evolution S-curves.

Diffusion Patterns

Diffusion patterns describe common themes that happen as trends diffuse through a population. They apply on the micro-level to individual population-segments, and on a macro-level to the overall population.

Diffusion of Innovation

The diffusion of innovation describes 5 separate stages of a diffusion curve: Innovators, Early Adopters,Early Majority, Late Majority, and Laggards. By understanding the traits of each of these groups, you can get a broad idea of what to expect, and how to slow or speed up adoption.

The Chasm

The Chasm describes a common constraint that occurs in a market segment between "early adopters" - who are willing to put up with a lot, and "early majority", who expect a lot. There is often a number of evolutionary constraints that must be broken through to bridge this single diffusion constraint and many new ideas, practices, and technologies get stuck in the chasm for that reason.

Evolution Patterns

Evolution patterns describe common ways that innovations evolve over time to become increasingly desirable. They apply on the micro-level to individual innovations within a trend, and on a macro-level to the evolution of trend as a whole.

Wardley Evolution

Innovations tend to go through four stages - the initial prototype, custom built versions, productized versions that compete, than comoditized versions that are all basically the same. By understanding where you are, you can understand the type of competition likely to happen, the types of processes likely to yield improvements, and large changes that will be needed to stick with the market.

Simplicity - Complexity - Simplicity

Innovations tend to start out relatively simple as a new approach to a problem. They become increasingly complex to cover more use cases and be more robust, and then become simple again as refinements are made and they're distilled to their essence.

Disruptive Innovation

Sometimes, innovations overshoot the mainstream populations needs on a particular dimension in order to be powerful for a particularly lucrative part of the population. In this case, these innovations or often overtaken by subsequent innovations that lower the performance on that dimension in order to raise it on other dimensions (example: Lower flexibility of a software product but raise the simplicity), these innovations can then "disrupt" the original innovation.

From the perspective a current innovation, the disruptive innovation appears to start below it in the s-curve, but it's able to gain adoption because the particular performance feature of that innovation is already higher than the market needs, and the new product competes on a different performance feature that is not even a target o

(image of how that plays out with S-Curves)

Gartner Hype Cycle

The Gartner Hype Cycle describes a particular way that the media over-inflates people's expectations of new innovations in comparison to how evolved they actually are for a particular market segment's needs.

Windermere Buying Hierarchy

The Windermere Buying Hierarchy describes four different improvement focuses that an innovation optimizes over time. First, it's trying to solve for functionality, then reliability, then convenience, and finally price. This loosely maps to the stages of Wardley Evolution.

(image here)


S-curves and s-curve patterns are a useful tool for quickly analyzing systems, particularly when looking at diffusion of trends and evolution of innovations. They can heuristically identify solutions and probabilities that would otherwise be quite time consuming to figure out using something like a full system or functional analysis.

Hopefully you find this tool useful in your quest to understand all the things.