PageBook · XLM/USDC · lot 10 XLM · quote in 7-decimal USDC

Four tick grids on one real market

A price grid decides which prices a maker may post. Drag the price and watch what each grid allows, how wide its tick is as a fraction of price, and how many level keys a taker must declare to cover one percent of depth. The cap is 200 writes per transaction.

0.500

Linear

Tick is a fixed 0.00001 USDC. Price of tick t is t × tick_size.

tick
tick / price
keys per 1% depth
next legal prices

Geometric

Each tick is 1 bps above the last. Price of tick t is 1.0001^(t − 2^21).

tick
tick / price
keys per 1% depth
next legal prices

5 significant figures

Five digits of the per-lot price. The tick grows tenfold at every decade.

tick
tick / price
keys per 1% depth
next legal prices

1-2-5 table

Five digits, but the tick is 1, 2 or 5 units depending on where in the decade the price sits.

tick
tick / price
keys per 1% depth
next legal prices

linear geometric 5 significant figures 1-2-5 table 200 writes per transaction

Tick width in basis points versus price for the four grids.
Tick as a fraction of price. Linear is a fixed quote amount, so on log axes it is a straight line falling tenfold per decade. Geometric is flat. The two digit-based grids are sawtooths: significant figures resets once per decade with a tenfold swing, the 1-2-5 table resets at 1, 2 and 5 with a 2.5-fold swing.
Level keys per one percent of depth versus price for the four grids.
Level keys for one percent of depth. A taker declares every level key in the band it may walk, and a transaction holds 200 writes. Linear crosses the cap at 0.20 USDC. Significant figures spends most of every decade above it. The 1-2-5 table exceeds it only between mantissas 40,000 and 50,000, and geometric never does.

What the ladders show

Each card lists the next five prices a maker may post above the chosen price. Linear steps by the same amount everywhere. The two digit grids step by one unit of the fifth digit, which means their ladders match linear's near the bottom of a decade and coarsen on the way up. Geometric's prices never end in a round number: every one of them would have to be rounded to atoms before it could be multiplied by a quantity, which is why PageBook's matching path rules it out.

At 0.158 all four grids agree to within a rounding, because the example market's linear tick was chosen for that price. At 6.3 linear needs over six thousand keys while the others are unchanged.