In generative art people talk about parameter space as the set of possible parameters for a generative system.

In statistics one can study the distribution of a random variable. Several models exist, the most common one being the normal distribution (or Gaussian distribution). When the distribution is known explicitly, it often depends on several parameters. A parameter space is simply the set of values that this parameter can take. For example, if we toss a coin, we can use the Bernoulli distribution of parameter $p$. In this case the parameter space is the intervall $*$.

More precisely, $\backslash Theta$ is a parameter space of dimension $p\backslash in\backslash mathbb\{N\}^*$ if there exists a $p$-dimensional vector space $E$ such that $\backslash Theta\backslash subseteq\; E$. $p$ is called number of parameters.

For example, $\backslash mathbb\{R\}\backslash times\backslash mathbb\{R\}^+$ is a parameter space because it is included in $\backslash mathbb\{R\}^2$. It is the parameter space for the normal distribution.

See also

• Parametric equation
• Parametric surface