critical systems

The
Spark.

Most sparks die. A few change everything. The difference is rarely the spark itself. It is the system surrounding it.

A spark can only travel as far as the system allows.

That is the idea.

Not every forest burns.

Not every idea spreads.

Not every technology becomes a standard.

The spark matters.

The structure matters more.

What seems to matter is connectivity.

Not the existence of a spark.

The existence of a path.

The forest

A forest does not burn because a spark exists.

Sparks are common.

Fire becomes possible when enough trees become connected.

For a long time, nothing happens.

Then a threshold is crossed.

The same spark that once disappeared now travels.

The model

This model is not scaled to real forests.

A step does not represent a fixed unit of time.

Instead, each step represents an opportunity: a tree may grow, lightning may strike, and a fire may spread.

The purpose is not to reproduce a specific forest. The purpose is to observe how connectivity changes outcomes.

Forest fire model

growth · lightning · connected burn

Chance an empty space becomes a tree.
Chance a tree is struck by a spark.
How many model steps run per frame.
Same rules. Different starting forest and random history.
42
TreeEmptyFireLightning
density
last fire
fires
steps

Results

many small fires · rare large fires

Fire Size Distribution0 fires
Recent fires

Most sparks produce small fires.

A few reach large connected regions.

The large fire is not caused by a special spark. It happens when ordinary lightning finds a connected forest.

The pattern

Ideas.

Technologies.

Markets.

Cities.

Networks.

The pattern repeats.

Connections accumulate gradually.

Propagation appears all at once.

The logic

The next step depends on the structure that already exists.

Connections create conditions for more connections.

Future Reach
=
Current Reach × (1 + Connectivity)

The equation is not a prediction.

It is a lens.

The spark may begin the process.

The network determines its reach.

What started the fire?

Or perhaps more importantly:

What made the forest ready to burn?

What in your world is quietly connecting — waiting for a spark?