How the fee works
Two parts, one fee
A transaction pays gasUsed × baseFee. The gas figure includes an L1 data component, but the L1 pricer currently charges so little per byte that this rounds to zero, so in practice the whole fee is the L2 base fee. There is no priority fee: bidding more does not move a transaction forward.
Constraints are backlogs
Instead of one gas target, the chain keeps several constraints. Each has a target rate (gas per second), a window (seconds) and a backlog (gas). Every block, each backlog is first paid down at its target rate for the seconds that passed, then every transaction's gas is added to every backlog. The exponent is the sum over constraints of backlog divided by target times window, and the base fee is the floor (0.02 gwei) multiplied by P4(x).
Long windows ratchet, short windows spike
A constraint with a day-long window reacts to the average demand: sustained load above its target grows the backlog for hours, and shedding it takes just as long. A constraint with a window of seconds reacts to bursts and drains almost immediately. Together they give a slow curve with sharp spikes on top.
No tips, first come first served
The sequencer orders transactions as they arrive and does not collect tips. eth_maxPriorityFeePerGas is zero. The only way to pay less is to wait for the backlogs to drain.
The owner can reset the backlogs
A call to setGasPricingConstraints replaces the constraint set and sets each backlog to the starting value supplied with it. The fee can therefore jump, up or down, at an owner action. Those actions are marked on the history charts and listed under owner actions on the live page.
P4 is a polynomial, not an exponential
P4 is the degree-4 Taylor expansion 1 + x + x²/2 + x³/6 + x⁴/24, evaluated in integer basis points. Near zero it tracks ex; above x ≈ 2 it falls behind and grows like x⁴/24. A backlog that would mean a 25× fee under a true exponential gives about 20× here.