Tessellations And Fractals Flashcards
This is created when a shape is repeated covering a plane without any gaps or overlaps
Tessellations
A pattern covering the plane by
fitting together replicas of the
same basic shape
Tessellation
Father of tessellation
Maurits Cornelis Escher
He elaborated tessellation as mathematical but artistic
Maurits Cornelis Escher
In geometrical terminology, a _____ is the pattern resulting from
the arrangement of regular polygons to cover a plane without any gap or overlapping. The patterns are usually repeating.
Tessellation
Three types of tessellations
•Regular
•Semi regular
•Demi-regular
This type of tessellation is made up of congruent sides and angles
Regular tessellation
polygons with congruent sides and angles
Regular polygon
What are the properties of a regular tessellation
- The tessellation must tile and fit with no overlapping/gaps
- The tiles must be regular polygons and all the same
- Each vertex must look the same
Pati kamo na guys di mani gami guro mag gwa sa exam
regular tessellations of two or more different polygons around a
vertex and each vertex has the same arrangement of polygons
Semi regular (Archimedean)
edge-to-edge tessellation, but the order or arrangement of polygon at each vertex is not the same
Cannot be named
Demi-regular tessellation
Mathematical constructs characterized by self-similarity
Fractals
Fractals are about four things:
• Fractions
• Functions
• Graphs
• Imaginary numbers
The latin wird for broken is ____
Fractus
They tend to appear nearly the same at different levels
Fractals
This is a discipline named and popularized by Benoit Mandelbrot
Fractal Geometry
What book did Mandelbrot write in 1197 na nag gwa sa module ni sir pake ko man sa iban
The Fractal Geometry of Nature
What are the two popular fractals
Sierpinski Triangle
Koch Snowflake
Repeating of a process over and over
Iteration
Following a rule repeatedly
Recursion
Distance between points
Scaling factor
Characteristics of a Fractal
- Self-similar
- Fractional Dimension
as one examines finer and finer details of the object, the magnified area is similar to the original
but is not identical to it
Self-similar
a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly
speaking, a fractal pattern) changes with the scale at which it is measured.
Fractional Dimension
