Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Interference and Diffraction02:18

Interference 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
Gestalt Principles of Perception01:21

Gestalt 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
Gauss's Law: Planar Symmetry01:27

Gauss'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
Shape and Texture of Coarse Aggregate01:25

Shape 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
Structures of Solids02:22

Structures 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
Properties of Fourier series II01:21

Properties 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...
805

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Beautiful Math, Part 6: Visualizing 4D Regular Polytopes Using the Kaleidoscope Principle.

IEEE computer graphics and applications·2017
Same author

Beautiful Math, Part 5: Colorful Archimedean Tilings from Dynamical Systems.

IEEE computer graphics and applications·2015
Same author

Beautiful math--aesthetic patterns based on logarithmic spirals.

IEEE computer graphics and applications·2014
Same author

Beautiful math, part 3: hyperbolic aesthetic patterns based on conformal mappings.

IEEE computer graphics and applications·2014

Related Experiment Video

Updated: Apr 30, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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.

Peichang Ouyang, Robert W Fathauer

    IEEE Computer Graphics and Applications
    |May 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    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.

    More Related Videos

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
    11:15

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

    Published on: May 30, 2016

    26.9K
    Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy
    05:24

    Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy

    Published on: January 10, 2025

    1.1K

    Related Experiment Videos

    Last Updated: Apr 30, 2026

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    42.6K
    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
    11:15

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

    Published on: May 30, 2016

    26.9K
    Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy
    05:24

    Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy

    Published on: January 10, 2025

    1.1K

    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.