Automatic generation of level maps with the do what's possible representation

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Automatic generation of level maps is a popular form of automatic content generation. In this study, a recently developed technique employing the do what's possible representation is used to create open-ended level maps. Generation of the map can continue indefinitely, yielding a highly scalable representation. A parameter study is performed to find good parameters for the evolutionary algorithm used to locate high quality map generators. Variations on the technique are presented, demonstrating its versatility, and an algorithmic variant is given that both improves performance and changes the character of maps located. The ability of the map to adapt to different regions where the map is permitted to occupy space are also tested.Final Accepted Versio

Billiard knots in a cylinder

We define cylinder knots as billiard knots in a cylinder. We present a necessary condition for cylinder knots: after dividing cylinder knots by possible rotational symmetries we obtain ribbon knots. We obtain an upper bound for the number of cylinder knots with two fixed parameters (out of three). In addition we prove that rosette knots are cylinder knots.Comment: 14 pages, 10 figures, to appear in the Journal of Knot Theor

The riddle of togelby

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.At the 2017 Artificial and Computational Intelligence in Games meeting at Dagstuhl, Julian Togelius asked how to make spaces where every way of filling in the details yielded a good game. This study examines the possibility of enriching search spaces so that they contain very high rates of interesting objects, specifically game elements. While we do not answer the full challenge of finding good games throughout the space, this study highlights a number of potential avenues. These include naturally rich spaces, a simple technique for modifying a representation to search only rich parts of a larger search space, and representations that are highly expressive and so exhibit highly restricted and consequently enriched search spaces. We treat the creation of plausible road systems, useful graphics, highly expressive room placement for maps, generation of cavern-like maps, and combinatorial puzzle spaces.Final Accepted Versio

Algebraic K-theory of stable ∞\infty-categories via binary complexes

We adapt Grayson's model of higher algebraic $K$-theory using binary acyclic complexes to the setting of stable $\infty$-categories. As an application, we prove that the $K$-theory of stable $\infty$-categories preserves infinite products.Comment: 20 pages; accepted for publication by the Journal of Topolog

Cauchy conformal fields in dimensions d>2

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d=3 and 4.Comment: 45 pages; v2: references adde

Influence of chance, history, and adaptation on digital evolution

We evolved multiple clones of populations of digital organisms to study the effects of chance, history, and adaptation in evolution. We show that clones adapted to a specific environment can adapt to new environments quickly and efficiently, although their history remains a significant factor in their fitness. Adaptation is most significant (and the effects of history less so) if the old and new environments are dissimilar. For more similar environments, adaptation is slower while history is more prominent. For both similar and dissimilar transfer environments, populations quickly lose the ability to perform computations (the analogue of beneficial chemical reactions) that are no longer rewarded in the new environment. Populations that developed few computational "genes" in their original environment were unable to acquire them in the new environment