Garden Creatures vs Stochastic Processes

Garden Creatures is an art experience to immerse players in the surreal, symbolic, and fantastical worlds of Hieronymus Bosch’s paintings. The experience combines exploration and artistic puzzles based on optical color mixing and figure rotation, offering a deep dive into the late medieval artist’s complex, thought-provoking works. Each level is inspired by Bosch’s masterpiece The Garden of Earthly Delights, with players exploring strange landscapes, interacting with characters, solving puzzles, and striving to bring color back to a world created by Bosch. The plot revolves around King Bird, a quirky monster who escaped the painting and stole the colors. As a player, you must follow the thief through mysterious, surreal places and help restore color to the painting! Features: • Richly Detailed, Mindful Experience Handcrafted visuals interpret the style of Bosch’s triptych. The aesthetics and pace create a calming, mindful environment that promotes focus and peaceful learning, blending art with fun. • Five Distinctive Levels Each level captures the bizarre and fantastical nature of Bosch's work, from dreamlike creatures to fantastical landscapes, while adapting them to fit modern audience's sensitivity. • Clever, Yet Accessible Puzzles Puzzles involve reconstructing elements of Bosch's work to progress in the experience, encouraging absorbing art through discovery. Recreating images from transparent color-field puzzle pieces requires planning ahead and breaking tasks into smaller steps. • Supporting Artistic Skills Development The puzzles are designed to enhance understanding of color theory through color mixing, as well as the painting process (e.g., starting with the background and finishing with the details). • Accessible Characters communicate using pictograms instead of typical dialogue, making the title accessible to a wider audience while introducing visual modes of communication. --- Note: Garden Creatures does not contain advertising, in-app purchases, or any other downloadable content.

The theory of stochastic processes is a method of describing time-dependent physical phenomena, based on probability theory, which allows the calculation of averaged macroscopic properties. The application allows for determining basic characteristics of stochastic processes, such as the mean or covariance function, as well as observing the evolution of the probability distribution. It also enables the stationarity of the studied process to be assessed, and for processes considered stationary, spectral analysis and the determination of correlation time. The application allows for the analysis of data from outside the program and the definition of one's own stochastic processes based on elementary processes. Both processes with a continuous set of values ​​and those assuming only discrete values ​​can be generated within the program. Specifically, when constructing a custom stochastic process, the user has access to basic processes such as the Brownian process, the Poisson process, and the α-stable Lévy process. Based on the stochastic process formula provided by the user, the program will generate a set of its realizations. The resulting set of time series (i.e., trajectories) of the given stochastic process is subjected to the analysis described above. To construct the trajectory, it is necessary to generate random variables derived from the appropriate probability distribution functions. The user can familiarize themselves with the basic types of random variables (i.e., uniform, Gaussian, exponential, Poisson, and α-stable distributions). In addition to numerical calculations, the user can also explore a theoretical introduction, which briefly discusses the basic division of stochastic processes into Markov and non-Markov processes. The theoretical discussion introduces the fundamental equations governing the dynamics of stochastic systems, such as the Fokker-Planck equation and the Langevin equation. The application also includes basic mathematical concepts related to the definitions of stochastic integrals, such as the Lebesgue-Stieltjes integral and the Ito integral. The user can also become familiar with the physical understanding of such Markov processes as the Brownian particle motion, the Ornstein-Uhlenbeck process, and the one-step process (represented by the Poisson process). The program also utilizes mathematical analysis tools such as Fourier analysis, both for the probability distribution function (determining the characteristic function) and the covariance function of the stationary process (spectral density). Spectral density allows for the determination of the noise type (white or colored noise).