This diagram is something that has occurred to me in the past, and continues to reoccur, so it seems worth mentioning. It gives a strong intuition about an otherwise seemingly complex topic: temporal, cyclical processes, and the changing trends within them.

The idea behind this diagram is to represent three dimensions: the cyclical nature of a given subject, the temporal quality of that subjects' cycles, and the evolutionary nature (or growth/decay if you will) of that subject over time. In some cases there might be a fourth dimension represent, but we’ll focus on these three.

Dialing it back

Now, it’s fairly common to see a diagram that demonstrates a cycle of some type. It can be purely logical, like a business process, or it can be something real and tangible, like the seasons of a year. Both of these represent some kind of cycle, but the number of discrete states/phases in that cycle can vary.

For example, a business might have twenty different “phases” of change for a given process, say how to complete some contractual obligation - but a year on Earth represents a fixed set of four seasons: spring, summer, fall, and winter.

Both of these examples represent the more common aspects: temporality (time) and cycle. And visually, they are represented as an actual cycle, typical with lines dividing up segments, and an “arrow of time” indicating the progress/change.

Adding in a new dimension

Now, what makes this diagram more interesting, and unique, is that as we add a new dimension, a new type of thinking and abstraction take place. The third dimension is a tapering of the spiral, upward. This produces the “helical” aspect, giving it a new way to represent changes in magnitude, and adding a new dimension of time, to complement the circular (cyclical) representation.

Before we could only represent a fixed cycle “length”, but now that can change, which represents the potential for a cycle’s behavior to change.

To be clear, the new diagram represents a discrete time step as each turn around a circle, and within that circle are N steps, part of the overall cycle. Moving up, along the circle in a helical fashion represents the change of another, greater time-step M.

So for example, a turn around the circle might represent 1 year, the height of the “helix” might represent 20 years. Then, the tapering or otherwise changing circumference of each year represents represents changes throughout the year, that might indicate volatility.

Recap: required data

The following data is required for the diagram:

1. The name/number of cycles for a given “unit” of time to pass (for example, the )
2. The discrete unit of time (e.g 1 second, 1 year, 1 century)
3. The dimension that rises and falls along each cycle and unit of time (e.g. stock market volatility, total population, weather temperature, popularity rating, etc…)