 In mathematics and particularly in dynamic systems, an initial condition 1 colon pages dot 160 in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time typically denoted t equals 0. For a system of ordered k the number of time lags in discrete time, or the order of the largest derivative in continuous time and dimension and that is, with n different evolving variables, which together can be denoted by n n dimensional coordinate vector generally n k initial conditions are needed in order to trace the systems variables forward through time. In both differential equations in continuous time and different equations in discrete time, initial conditions affect the value of the dynamic variables state variables at any future time. In continuous time, the problem of finding a closed form solution for the state variables as a function of time band of the initial conditions is called the initial value problem. A corresponding problem exists for discrete time situations. While a closed form solution is not always possible to obtain, future values of a discrete time system can be found by iterating forward one time period per iteration, the rounding error may make this impractical over long horizons.