Pattern formation is widely observed in nature. One organism that shows spectacular patterns is Dictyostelium discoideum (D.d.). When nutrients are available in plenty, D.d. lead solitary lives - they feed and divide. However, when a population of D.d. begins to starve, the cells become social. Each cell emits a chemical called cyclic adenosine monophosphate (cAMP), which diffuses in the medium. When neighboring cells detect cAMP, they also secrete cAMP. An enzyme phosphodiesterase, secreted by the cells, degrades cAMP. The system is therefore a reaction-diffusion system. After a few hours of signaling, the response of the cells to cAMP is seen either as large scale spiral waves or target patterns. The waves persist for about 2h. Towards the end, the cells aggregate towards the centers of the spirals and targets through chemotaxis and form mounds. These mounds can form multi-cellular slugs which move around looking for food. Failing to find food, the slug transforms into a fruiting body with spores on the top. D.d. is thus a unique organism that exhibits unicellular and multicellular behavior. In this thesis, I analyze the effect of various parameters on the patterns formed by D.d.. As D.d. starves, its internal biochemistry changes. This developmental changes drastically affect the patterns. I will present results of a systematic analysis of the effects of the developmental path on pattern formation. Next, I considered the effects of variability in parameters in a population on the patterns. By mixing two populations at different developmental stages, I introduced developmental variability in the population and found that the patterns depend on the heterogeneity in the biochemical parameters and in spatial distribution of cells. By modifying an existing model, by introducing temporal variations of certain biochemical parameters, I was able to simulate the experimental results. Further, using the simulations I was able to determine that the dynamics of the starving populations changes from being excitable to oscillatory. This work proved that a systematic analysis of patterns can provide information about the developmental pathways in a system. Using the idea that populations at different developmental stages form different patterns, I performed experiments to check for the existence of “memory.” Indeed, I found that populations have a memory of starvation for about 1 h. These results indicate that the biochemical parameters do not deregulate at the same time. Simulations of the model that I modified confirmed this analysis. In a population, the amount of cAMP produced by cells varies. Despite this variation, the signaling mechanism is robust. Experiments to understand this robustness revealed that signaling can occur at very low amounts of cAMP. In fact, when a low density population of wild type cells that could not aggregate on its own was mixed with a high density population of mutants that could not produce cAMP, the resulting mixture aggregates. Counterintuitively, rather than a lack of cAMP, this effect was because of insufficient amount of the enzyme, phosphodiesterase, which degrades cAMP. Estimates of the degradation rates confirm that phosphodiesterase is necessary for wave propagation. In nature, the cells have to survive on various kinds of substrates. To understand the importance of substrates for pattern formation, I performed experiments to observe their effects. I used agar gels of various densities as the substrate and found that as the density of the agar substrate increased the patterns needed more time to form, and a transition from spirals to targets was observed. However, if the cells are immersed in larger amounts of buffer, the effect vanishes. I hypothesize that this could mean that the thin layer of buffer over the cells is very important. In all the simulations, I have varied the parameters by hand. To establish a mathematically rigorous method to estimate the parameters, I have worked with different methods of coupling data to models to optimize the parameters.