When the human mind searches concept space for solutions to a given condition we have a choice between conventional and creative thinking. But what are the probabilities of improving a given situation using creative thinking compared with conventional thinking? To answer this question we are extending the meaning of creativity beyond human creativity. We view creativity as an optimised search strategy applicable to the larger set of all teleonomic systems and term this creativity teleonomic creativity. We argue that an analog process is common to all manifestations of creativity within teleonomic systems and describe this process and its cause. In order to show this process and to make quantitative comparisons, we utilise the metaphor of an adaptive fitness landscape and simple statistical techniques. The term fitness in our case describes the condition of a well-defined property being suitable for a purpose, rather than an overall evaluation of many complex interactions measuring reproductive success. We define creativity as the successful attempt of either individuals or populations to gain higher fitness via exploration of global fitness peaks as opposed to the exploitation of a currently occupied local peak. We then show mathematically how the inclusion of creativity in a search can dramatically increase the chances of finding appropriate solutions. We also recognise that creative behaviour is most successful when the environmentis unstable. We note the existence of a strategic meta-parameter that allows self-adaptation when tuned via a feedback loop from the environment. We show that creativity can be understood as a random process with an optimal setting for the standard deviation that maximises the probability of hitting a target of higher fitness. We support our claims with computer simulations and observe several occurrences of teleonomic creativity in nature. In addition we measure the entropy of a teleonomic system via the phase-space of internal variables and observe a sudden entropy increase during the onset of creative behaviour in a teleonomic system. Our investigations also enable us to rationalise the processes, conditions and phenomena surrounding human creativity such as mistakes, madness, serendipity, humor, analogy making and interpret the function of creativity promoters and inhibitors. Our findings may also allow us to incorporate creativity into artificial computer models. We speculate that creativity is an emerging property of any teleonomic system and as such ubiquitous in nature.