149. The world in a grain of sand: fractal stories

Since classical times and Aristotle’s Poetics, we have believed that stories must have a beginning, middle, and end. Even with distortions of the timeline such as flashbacks and flashforwards, such stories move with inexorable causality from their starting conditions to the final consequences. And this does create extremely satisfying tales. But what if we try to imagine a form of story-telling that is divorced from the iron hand of time and from the laws of cause and effect?

Looks like

What, for example, if the organizing principle of a story is homologies? Homology just means a likeness in structure. For example, we might say that confectionary with a liquid centre is a homologue of our planet with its molten core.

This idea of homology might seem unusual in our era of scientific understanding of cause and effect. But it’s a very old idea. For much of the Middle Ages, scholars attempted to understand the universe using this principle. For example, believing that there was a principle of homology between the earthly and the heavenly realm, healers felt that God had created a medicinal plant for every ailment, and that these plants could be recognized by their “signatures”.

The white spotted leaves of lungwort were used to treat tuberculosis because they were thought to look like diseased lungs.

Satin Island by Tom McCarthy is a good literary example of the use of this principle of homology. The narrator is charged by a mysterious multi-tentacled consultancy firm to create a report on the codes governing the present age. He finds connections and patterns everywhere, and therefore perhaps, nowhere.


Connections and patterns everywhere. That’s a characteristic of fractals. Fractals are mathematical entities, repeating patterns. Whatever level of magnification you look at them, they go on and on forever.

How cool would that be for a story to exhibit the same pattern wherever you looked? To go on and on forever? Of course, stories have endings. But their resonances in the reader’s mind may persist as long as that brain exists.

There are various ways in which stories can have this fractal-like effect. Let’s consider them, one by one.

  • The reader’s experience of structure. This is different from the writer’s conscious use of structure, in that it is not usually deliberative. Let’s look at this first in an analytical mode, the mode the writer uses. Different writers follow different conventions about how a story is structured. But common terms include scenes, sequences and acts. Some include the notion of beats as the smallest atomic unit of dramatic writing. What all of these have in common, is a change in tension. There is an incident, a rise in tension and a resolution. This creates change and movement. This general formula can be applied from the smallest unit of story (the beat or scene) all the way to the arc of the entire narrative. In a sense, this repeat pattern is fractal. Maslow’s famous triangle illustrates this at the level of the whole story.

Now let’s examine the reader’s experience of this structure. There’s a rhythmic rise and fall of tension building to a crescendo. Though the reader may not be aware of the units of the rhythm, the body experiences it.

  • The most literal fractal story would be one which exactly repeats at every level. Nancy Fulda describes what this would be like: “Having a novel about a Father who loses his son, in which a father loses a son in each chapter, is not going to go over real well unless it’s some sort of an artsy/literary thing.” But she says, at the level of thematic similarity, something like this is possible: “A novel with a theme of loss might have an overarching storyline that addresses that theme, coupled with several subplots that address it in different ways, coupled with word choices at the sentence level that also emphasize the theme. That’s a pattern that starts to sound distinctly fractoid.” We might also explore an idea at different “scales”. Are children learning the same lessons as their parents? Is the family going through the same seismic shifts as the country they live in? I’m indebted to A.C. Blais for this idea.
  • Symmetry. Our brains like and respond to symmetry. Stories that loop back to their beginnings (either as a circle or a spiral) are very satisfying. The Hobbit is a  classic “there and back” tale. The widely-used, if rather mechanical, Hero’s Journey format is full of symmetries in which different segments mirror each other.

A more complex mirroring occurs in David Mitchell’s Cloud Atlas, a nested series of two-part stories.

  • Echoes and motifs. This is a more subtle (and less geometrical) example. When themes and images recur throughout a story, our brains register the pattern (though not always consciously). Pattern is one of the main ways in which we understand the world. In the case of echoes and motifs, the pattern is not an exact repeat, but it creates an atmosphere laden with meaning. Consider, for example, The Great Gatsby. Arguably, the novel charts the hollowness of The American Dream. Recurring motifs underly this—the parties, the conspicuous consumption, the transactional nature of relationships, the optometrist’s eyes, the valley of ashes.

Counterposed to these is the green light, which represents for Gatsby all that is unattainable and all that he has lost.

A fractal story grid

How might we apply these ideas to the construction of a story? This must start with the fundamental pattern that will be repeated and echoed. Let me take the premise of the novel I’m working on:  Sol must learn that boundaries do not provide safety, or he will never make it home.

With this, I can set up a grid: bounded vs unbounded and safe vs unsafe. This is the primary pattern that will repeat again and again at smaller and smaller scales.

Next, I identify some of the plot elements. Sol, the central character, is a clever boy who will grow to manhood over the course of the story. He will transgress boundaries and discover things. And he will struggle with his feelings of loss and detachment. So, within the basic grid I can place a further four elements: knowledge, activity, time and feeling.

And I can break each of these four elements down into four sub-elements, as you can see below. This approach is modified from the system promoted by Dramatica.

In each grid and sub-grid, the top left will have the valency of bounded and safe, the top right of bounded and unsafe, the bottom right unbounded and safe, and the bottom left unbounded and unsafe. So, for example under Feeling (which is predominantly unbounded and unsafe), secure is safe and bounded, while insecure is unsafe and unbounded. There is a dramatic tension between elements in each grid and sub-grid that are diagonally opposite each other. This tension will supply the rhythm of the story.

This is not the structure of the story. It’s a coding sheet. When the plot points are superimposed onto the grid, it shows the valency of each point and the connection with other points. This helps guide the sculpting of the piece to achieve the desired effect.

For example, in the beginning of the novel, Sol is evacuated during a war to his uncle’s house in the country. He desperately misses his parents and believes he has found the sign of a way to get back to them. So the story begins in the bottom right quadrant of feeling with a sense of detachment. He fails to bond with his uncle, Zand but, when he crosses the boundary wall of the estate, he encounters a beekeeper, Bernard, with whom he forges a relationship.

There is a recurring theme of boundaries. Zand tells him he is free to go anywhere in the house, except in the study. Sol is fascinated with the beehive with its many chambers. In the field by Bernard’s hives he discovers what he believes to be a shape under the ground.  We have moved to the top left set of quadrants dealing with knowledge.  Is the shape really there? Or is it an illusion? Can he reason it out, or will he need to apply the less secure means of intuition? The shape escapes the boundaries of the present takes us into the past (bottom left quadrants dealing with time) when he comes to believe he is looking at the  outline of the walls of an old Anglo-Saxon meeting place, a wintan. The assignation of the place to the past puts it in the sub-quadrant which is bounded and safe. It is the present which is unbounded and unsafe.

The final act of the book is where certainty vanishes. It takes place largely in the activity quadrant and is dominated by the contradiction between the discrete and the diffused.

New and different stories

So, it could be done. The question is why would anyone do it? Well, as a display of virtuosity perhaps. This is arguably the motivation behind David Mitchell’s Cloud Atlas. But, there are two more important reasons. The first is to give the reader the pleasurable experience of pattern and rhythm. The second, and most important, is that it carries the message of the book. The message is that there are no bounded spaces which are inherently safe for Sol. If the fractal pattern is self-similar all the way down to the smallest level of magnification, then no space is without peril. The advantage of considering fractals as a basis for story-telling is that it may open the door to new and different kinds of stories.

A final point. I’m not suggesting this as a grand scheme for the construction of stories. Grand schemes tend to lead to mechanical cloned stories. This is just the schema that I developed to help me tell this particular story.

3 thoughts on “149. The world in a grain of sand: fractal stories

  1. Very interesting, Neil. I’ve seen the movie Cloud Atlas and really enjoyed the way it was set up. I’m guessing the book is even better at it. It sounds like a form of syllogism?


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