Ticks are the fundamental unit of accounting within the dex. Each tick is an integer between 559,680 and -559,680. All tradeable liquidity, in the form of either PoolReserves or LimitOrderTranches is stored at a specific tick. Price for liquidity held at a tick is stored in the form of MakerPrice — the price at which the MakerDenom is being sold denominated in terms of the TakerDenom. The MakerPrice of liquidity being stored at tick i is determined by the function:p(i)=1.0001iSome examples:
Price of tick 0: p(0)=1.00010=1
Price of tick 1: p(1)=1.00011=1.0001
Price of tick -1: p(−1)=1.0001−1=≈0.9999
Price of tick 4000: p(4000)=1.00014000≈1.4918
Price of tick -4000: p(−4000)=1.0001−4000≈0.6703
MakerPrice can also be seen as the rate for converting MakerDenom to TakerDenom:MakerDenom⋅MakerPrice==TakerDenom.Conversely, we can convert TakerDenom to MakerDenom as follows:MakerPriceTakerDenom==MakerDenom.Given an intent to deposit ATOM and USDC into a pool (assuming no fee) with the Price of ATOM set at 10 USDCperATOM and implying a reciprocal USDC price of 0.1 ATOMperUSDC, the best tick index to deposit to will be +/-23027 given that the target price is 10. (we are selling 1 ATOM for 10 USDC)USDC liquidity will be placed at tick -23027, which implies a price of 1.0001−23027 = 0.1ATOMATOM liquidity will be placed at tick +23027, which implies a price of 1.000123027 = 10USDCA good way to think about price in this context is how much of TakerDenom Alice would receive if she sold a single MakerDenom and vice versa. In this case, she would receive 10 USDC given an input of 1 ATOM, and 0.1 ATOM given an input of 1 USDC.From this, the simple price heuristic is How much output given unit input.swapping 100 USDC for Atom: 100⋅MakerPrice(USDC)=100∗0.1=10ATOMswapping 100 Atom for USDC: 100⋅MakerPrice(ATOM)=100∗10=1000USDC
