Related Experiment Video
Updated: Apr 30, 2026
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
42.6K
Beautiful math, part 2: aesthetic patterns based on fractal tilings.
IEEE Computer Graphics and Applications
|May 9, 2014
Summary
This study introduces novel fractal tilings (f-tilings) with fractal boundaries, generated using a single prototile and scaling factor. These f-tilings enable the creation of intricate, seamless colored patterns through invariant mappings.
Area of Science:
- Geometry
- Tessellation Theory
- Fractal Geometry
Background:
- Fractal tilings (f-tilings) are geometric arrangements where the boundary exhibits fractal properties.
- Previous research has explored various tiling methods, but rare families of f-tilings remain underexplored.
Purpose of the Study:
- To present two new families of infinitely many fractal tilings.
- To demonstrate a method for generating seamless, colored patterns from these f-tilings.
Main Methods:
- Construction of f-tilings using a single prototile (a segment of a regular polygon) and a fixed scaling factor.
- Development of invariant mappings to automate pattern generation.
Main Results:
- Successfully generated two distinct families of rare, infinitely many f-tilings.
- Demonstrated the capability to produce appealing, seamless, and colored patterns from the constructed f-tilings.
Conclusions:
- The presented method offers a novel approach to creating complex fractal tilings.
- Invariant mappings provide an effective tool for generating intricate visual patterns from geometric constructions.
Related Concept Videos
02:18Interference and Diffraction
28.7K
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
28.7K
01:21Gestalt Principles of Perception
1.8K
Gestalt principles provide a framework for understanding how humans perceive objects as unified wholes within their context. These principles are essential in explaining the cognitive processes that make sense of complex visual stimuli by organizing them into coherent groups. One fundamental principle is proximity, which posits that objects located close to each other are perceived as a collective group. For instance, when dots are positioned near one another, the visual system interprets them...
1.8K
01:27Gauss's Law: Planar Symmetry
7.6K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.6K
01:25Shape and Texture of Coarse Aggregate
1.3K
Aggregate shape is classified based on the relative sharpness or roundness of the edges and corners. This classification includes categories like rounded, angular, elongated, and flaky, each with specific characteristics. Rounded aggregates, fully shaped by attrition, are typical of river or seashore gravel, while angular aggregates, such as crushed rock, have well-defined edges. Aggregates that are elongated and flaky are less desirable, as they can reduce the workability and strength of...
1.3K
02:22Structures of Solids
17.8K
Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
17.8K
01:21Properties of Fourier series II
805
Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
A function f(t) is...
805