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Reconfigurable multiple-input multiple-output can provide performance gains over traditional MIMO by reshaping the channels, i.e., introducing more channel realizations. In this paper, we focus on the achievable rate maximization pattern design for reconfigurable MIMO systems. Firstly, we introduce the matrix representation of pattern reconfigurable MIMO (PR-MIMO), based on which a pattern design problem is formulated. To further reveal the effect of the radiation pattern on the wireless channel, we consider pattern design for both the single-pattern case where the optimized radiation pattern is the same for all the antenna elements, and the multi-pattern case where different antenna elements can adopt different radiation patterns. For the single-pattern case, we show that the pattern design is equivalent to a redistribution of gains among all scattering paths, and an eigenvalue optimization based solution is obtained. For the multi-pattern case, we propose a sequential optimization framework with manifold optimization and eigenvalue decomposition to obtain near-optimal solutions. Numerical results validate the superiority of PR-MIMO systems over traditional MIMO in terms of achievable rate, and also show the effectiveness of the proposed solutions.