Sierpiński triangle - Wikipedia
网页Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.
Barnsley fern - Wikipedia
网页The fern is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Like the Sierpinski triangle, the Barnsley fern shows how graphically beautiful structures can be built from repetitive uses of mathematical formulas with computers.
Advancing mathematics by guiding human intuition with AI
网页2021年12月2日 · We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these ...
[2409.20458] Uncovering Hidden Patterns: Approximate …
网页2 天之前 · We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel-Padé approximant and classical analysis to determine the analytic ...
Sequences and Patterns – Mathigon
网页Learn how to find and analyse patterns in mathematics, and how they can be used in various fields. Explore examples of simple and complex sequences, and discover the Fibonacci sequence and Pascal's triangle.
Fractal - Wikipedia
网页A fractal is a geometric shape with detailed structure at arbitrarily small scales, often having a fractal dimension exceeding its topological dimension. Learn about the history, types, and applications of fractals in mathematics, nature, art, and chaos theory.
General Pattern Theory: A Mathematical Study of Regular …
网页1994年1月20日 · The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically …
网页Scientists could create patterned biomaterials—which are made from living things and could degrade faster than synthetic materials such as plastic—with desired properties. For example, they could...
Pattern Recognition | Introduction - GeeksforGeeks
网页Pattern is everything around in this digital world. A pattern can either be seen physically or it can be observed mathematically by applying algorithms. ... an appropriate class label …
Medical Image Segmentation with SAM-generated Annotations
网页2 天之前 · The field of medical image segmentation is hindered by the scarcity of large, publicly available annotated datasets. Not all datasets are made public for privacy reasons, and creating annotations for a large dataset is time-consuming and expensive, as it requires specialized expertise to accurately identify regions of interest (ROIs) within the images. To address these challenges, we evaluate ...