MARZIEH ZAREThe thinking behind the thinking
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The inner worldJUNE 2026Essay

Fractals of the Self

You are not a machine, you are weather. The same mathematics that describes a brain near criticality, scale-free, self-similar, poised at the edge of chaos, describes a healthy mind. And it says the thing my criticality work keeps saying: the good states live at the edge, not the extremes.

Ernst Haeckel, radiolaria (Stephoidea) from Kunstformen der Natur (1904). Public domain, via Wikimedia Commons.

The Western mind loves machines. Predictable, linear, controllable: push button A, get result B. It is a comforting picture of the self, and it is wrong. You are not a machine. You are closer to weather.

A thunderstorm, an ecosystem, an economy: these are complex systems, and so are you. Their behavior does not decompose into the behavior of their parts. Water molecules are not wet; wetness emerges from how they interact. Neurons are not conscious; consciousness emerges from their patterns. And your self is not located in any single thought, memory, or belief. It is the pattern of relationships among all of them. That single shift, from machine to complex system, changes what it means to work on yourself.

I want to make the shift concrete, because I spend my research life measuring exactly this kind of structure in the brain, and the same measurements read a life with unsettling accuracy.

The self is a scale-free network

Start with the shape. Your inner world is a network: nodes (memories, beliefs, emotions, roles) joined by edges (the associations that make one thing call up another). And the network is not democratic. It is scale-free, which means its connections follow a power law: a few nodes are enormously connected while most have only a handful.

Those few are the superhubs. A single early experience can wire itself to hundreds of later fears and behaviors. One core belief, “I am unworthy,” can quietly bias thousands of daily decisions. Networks like this, the ones Barabási and others described for the web and the cell, have a characteristic pair of properties, and both are true of you. They are resilient to random damage: lose a scattered set of memories and you remain yourself. And they are fragile at the hubs: damage a core attachment or a foundational belief and the change cascades system-wide. That fragility is also the leverage. You do not have to renovate everything. You have to find the hubs.

The network is also a small world. Any state is a few associations from any other. You smell coffee, which recalls a café, which recalls a conversation, which opens onto an old grief, and in five short jumps breakfast has become a bad afternoon. The same topology that makes you vulnerable to those cascades means that a resource, a calmer state, a different self, is also only a few connections away. Transformation is closer than it feels.

It behaves like weather, not clockwork

Now the dynamics. Complex systems are nonlinear: cause and effect are not proportional. A tiny trigger can set off an emotional avalanche. Years of effort can produce nothing visible, then a single conversation reorganizes a worldview overnight. This is not a sign that something is broken. It is what these systems do.

They have attractors, the states they keep rolling back into. Some are point attractors, a baseline mood that reasserts itself after any disturbance. Some are cyclic. The most interesting are strange attractors: never exactly repeating, but staying within a recognizable range, the way your moods vary unpredictably yet remain unmistakably yours. Every attractor is a valley in the landscape, and the depth of the valley is how much energy it takes to climb out. A passing mood is a shallow dip. A depression is a steep basin, and telling someone to just step out of it misunderstands the terrain.

And they have phase transitions. Water does not gradually become ice; at zero degrees it changes state all at once. Minds do the same. Pressure accumulates invisibly, a threshold is crossed, and the whole system suddenly reorganizes: the breakthrough, the collapse, the falling in love that rearranges every priority. Change often looks impossible right up until it looks inevitable, because the system has to reach critical conditions before it turns.

The edge of chaos is criticality

Here is where the essay meets my day job.

Complex systems are most alive at what the complexity literature calls the edge of chaos: the narrow zone between rigid order and pure randomness. Too far toward order and the system is frozen, brittle, unable to adapt. Too far toward disorder and it is noise, unable to hold a pattern long enough to mean anything. At the edge, and only at the edge, a system is both stable and flexible, both integrated and open, maximally able to respond.

In neuroscience this edge has a precise name. It is criticality: the regime near a phase transition where brain activity becomes scale-free, where fluctuations reach across time and space, where the system is poised to react to the smallest relevant input. Measuring how close a brain sits to that critical point is a large part of what I do. And the finding that keeps recurring is that health is not maximal order. It is poise near the transition.

The mind obeys the same law. A life tuned too far toward order shows up as rigidity: compulsive routine, perfectionism, hyper-control, a self so defended it cannot grow. Tuned too far toward disorder it shows up as fragmentation: no structure, no follow-through, affect with nothing to contain it. The states worth wanting are not at either pole. They are at the edge, where there is enough structure to hold you and enough looseness to let you change. When people say they feel most themselves in a state that is stable but not stuck, that is not a metaphor. That is the signature of a system near criticality.

Self-similar, across scales

One more property, the one in the title. Living structures are self-similar: they have detail at every level of magnification, and the pattern rhymes across scales. A life vision connects to yearly goals connects to monthly projects connects to today’s small task. A core value informs a principle informs a passing thought informs a single sentence you say out loud. Zoom in or out and you see the same organizing shape. This is what a fractal is, and it is why a change at one scale can propagate to the others: the daily practice is not separate from the life, it is the life at a smaller magnification.

What follows

If the self is a scale-free, near-critical, self-organizing system rather than a machine, then the whole logic of working on it changes.

You cannot control it directly, and trying tends to backfire, because control pushes toward the rigid pole and the rigid pole is where systems die. What you can do is shape conditions and let the system reorganize: create the feedback, remove the block, and trust the self-organization. You look for hubs and bifurcation points, the moments and nodes where a small, well-placed change has outsized effect, instead of spreading effort evenly over a surface. And you stop expecting a straight line. Progress in a complex system is spirals, plateaus, and sudden leaps, and a long flat stretch is often pressure accumulating toward a transition, not failure.

I spend my days quantifying how near a brain sits to its critical point. The strange gift of that work is how well the same yardstick reads a life. The self worth building is not the most controlled one, and not the most spontaneous. It is the one held at the edge, structured enough to stand, loose enough to move, where the interesting things have always happened.