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In this chapter and the two following ones we will discuss two methods for estimating the dimension and entropy spectra from a time series. Both methods use information from distances between points in phase space. Nearest neighbour methods are based on a fixed number of distances within a ball around reference points. The dimension and entropy spectra can be estimated using an expression for the expectation of the powers of the distance to the $k$-th nearest neighbour of a reference point. In the next section, we show how such an expression can be derived. The result can be used in several ways to obtain estimators for the dimension function; these options are discussed in section 3.3. In section 3.4 we demonstrate how to use the nearest-neighbour algorithm with the Rössler attractor. Finally, we briefly describe the current implementation of the estimator algorithms in section 3.5.