Diffusion, explained.
Diffusion is the spreading of a concentration through local random motion or equivalent concentration-gradient transport.
Why it happens
More material leaves a highly concentrated cell than arrives from a dilute neighbor. The net result smooths differences even though the underlying movement need not aim toward emptier locations.
Diffusion redistributes material down concentration gradients through local movement, without requiring directed motion toward a destination.
Read the result
Advance the mixing steps and watch the central concentration fall while neighboring concentrations rise. The total remains one hundred because the row is closed; no dye is allowed to escape its boundaries.
A worked example
One step from a concentrated center
A single central cell starts with one hundred units.
One step retains sixty centrally and moves twenty to each adjacent cell.
The distribution changes but the total remains one hundred, separating spreading from loss of material.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A closed 21-cell row starts with 100 units in the center. Each step transfers 20% to each available neighbor and retains the rest; boundary cells retain the share that cannot leave.
Where this idea is useful
A practical use
A localized concentration spreads across a closed region while its total material is conserved.
A common misconception
“A falling local concentration means material disappeared.”
Material can move elsewhere. Distinguish local concentration from the total across the system and any flow through its boundaries.
What this explanation leaves out
- One-dimensional discrete mixing omits flow, reactions and material-specific coefficients. Time steps are illustrative.
Why does the boundary retain some dye?
The closed-row rule keeps the outward share inside, ensuring conservation rather than simulating an absorbing boundary.
When a quantity falls in one location, where could it have moved?
Further reading
Explore the original research or the teaching reference behind this experiment.