We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.

Let {ξ(n)}n∈Z be a two-color random scenery, that is, a random coloring of Z in two colors, such that the ξ(i)’s are i.i.d. Bernoulli variables with parameter 1 2 . Let {S(n)}n∈N be a symmetric random walk starting at 0. Our main result shows that a.s., ξ ◦ S (the composition of ξ and S) determines ξ up to translation and reflection. In other words, by observing the scenery ξ along the random w...

At large scale, landscapes result from the combination of two major processes: tectonics which generate the main relief through crust uplift, and weather which accounts for erosion. This paper presents the first method in computer graphics that combines uplift and hydraulic erosion to generate visually plausible terrains. Given a user-painted uplift map, we generate a stream graph over the enti...

Generation and real-time rendering of terrain is a complex and multifaceted problem. Besides the obvious trade-offs between performance and quality, many different generation and rendering solutions exist. Different choices in implementation will result in very different visuals, usability and tools for generation. In this thesis, a fast and intuitive terrain generation method based on sketchin...

We report a novel illusory distortion of the visual scene, which became apparent during both: (i) observer rotation inside a furnished stationary room; and (ii) room rotation about the stationary observer. While this distortion had several manifestations, the most common experience was that scenery near fixation appeared to sometimes lead and other times lag more peripheral scenery. Across a se...

This article reviews recent findings indicating some common brain processes during dissociative states and dreaming with the aim to outline a perspective that neural chaotic states during dreaming can be closely related to dissociative states that may manifest in dreams scenery. These data are in agreement with various clinical findings that dissociated states can be projected into the "dream s...