Dynamics on space-filling shapes

现代科学的力量来源于数学模型和工具，这些模型和工具使我们能够预测它们的行为。该项目旨在构建由动态系统给出的新模型，该系统在称为多面体的高维形状晶格中从一个瓷砖持续移动到另一个瓷砖。预计该结构将导致具有属性的新功能，这些功能将提供当前增长过程模型的扩展。该项目的预期成果包括描述非线性特殊函数的预测工具和有关其对称性减少的信息。这将带来显著的好处，如新的数学知识、创新技术和提高澳大利亚的科学能力。

Modern science derives its power from mathematical models and tools that enable us to predict their behaviours. The project aims to construct new models given by dynamical systems that move consistently from one tile to another in a lattice of higher-dimensional shapes called polytopes. The construction is expected to lead to new functions with properties that will provide extensions of current models of growth processes. The intended outcomes of the project include predictive tools that describe nonlinear special functions and information about their symmetry reductions. This should provide significant benefits, such as new mathematical knowledge, innovative techniques, and enhanced scientific capacity in Australia.