Histogram mapping synthesis (HMS) is a new technique for sound design based on cellular automata (CA). Cellular automata are computational models that create moving images. In the context of HMS, and based on a novel digital signal processing approach, these images are analyzed by histogram measurements, giving a sequence of histograms as a result. In a nutshell, these histogram sequences are converted into spectrograms that, in turn, are rendered into sounds. Unlike other CA-based systems, the HMS mapping process is not intuition-based, nor is it totally arbitrary; it is based instead on resemblances discovered between the components of the histogram sequences and the spectral components of the sounds. Our main concern is to address the problem of the sound-design limitations of synthesis techniques based on CA. These limitations stem, fundamentally, from the unpredictable and autonomous nature of these computational models. As a result, one of the main advantages of HMS is that it affords more control over the sound-design process than other sound-synthesis techniques using CA. The timbres that we have designed with HMS range from those that are novel to those that are imitations of sounds produced by acoustic means. All the sounds obtained present dynamic features, and many of them, including some of those that are novel, retain important characteristics of sounds produced by acoustic means.