6 citations · 9 across the 4 of their papers we have counts for
6 papers
Existence of Life in Lenia
Craig Calcaterra, Axel Boldt
Lenia is a continuous generalization of Conway's Game of Life. Bert Wang-Chak Chan has discovered and published many seemingly organic dynamics in his Lenia simulations since 2019.…
An Itô calculus for a class of limit processes arising from random walks on the complex plane
Stefano Bonaccorsi, Craig Calcaterra, Sonia Mazzucchi
Within the framework of the previous paper [8]. we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study…
Approximating with Gaussians
Craig Calcaterra, Axel Boldt
Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are give…
Foliating Metric Spaces
Craig Calcaterra
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and…
Lipschitz Flow-box Theorem
Craig Calcaterra, Axel Boldt
A generalization of the Flow-box Theorem is given. The assumption of continuous differentiability of the vector field is relaxed to a local Lipschitz condition. The theorem holds i…
Metric Coordinate Systems
Craig Calcaterra, Axel Boldt, Michael Green +1
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian…