Swastika Tiling

An implicit curve: swastika(x,y) = 0

The swastika here is an ancient Buddhist symbol, not the Nazi one.

Composition of swastika(x,y), arctan(x) and tan(x)

(k = 0.25)

Composition of swastika(x,y), arctan(x) and tan(x)

(k = 0.125)

Composition of swastika(x,y), arctan(x) and tan(x)

(k = 0.4)

Composition of swastika(x,y), arcsin(x) and sin(x)

(k = 0.25)

Composition of swastika(x,y), arcsin(x) and sin(x)

(k = 0.4)

Swastika of Swastikas

(k = 1/4, 5/24)

Swastika of Swastikas of Swastikas

(k = 1/4, 1/4, 5/24)

Swastika of Swastikas of Swastikas

(Unicode of 卍: 0x534D)

A Maze of Swastikas

(k = 0.1)

( Mathematical software used: Graph )


Related posts:

• Swastika (卍)

Tiling using Rounded Crosses

( Mathematical software used: Graph )


Related posts:

• Rounded Cross
• Tiling using Nested Crosses

Tiling using Spiral Hexaskelions

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.25.

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = golden ratio ~ 0.618.

The spirals are Archimedean spirals.

(1 < number of spiral turns < 2)

The spirals are Archimedean spirals.

(2 < number of spiral turns < 3)

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.05, 0.1, 0.15, 0.2, ..., 0.8.

( Mathematical software used: GeoGebra )

Tiling using Nested Stars (2)

(A) Tiling using Nested Six-Pointed Stars (and Nested Triangles)

(Clockwise Stars)

(Counterclockwise Stars)

(Type 1: Clockwise Stars & Clockwise Triangles)

(Type 2: Clockwise Stars & Counterclockwise Triangles)

(Type 3: Counterclockwise Stars & Clockwise Triangles)

(Type 4: Counterclockwise Stars & Counterclockwise Triangles)

(Type 1: Clockwise Stars & Clockwise Triangles)

(Type 2: Clockwise Stars & Counterclockwise Triangles)

(Type 3: Counterclockwise Stars & Clockwise Triangles)

(Type 4: Counterclockwise Stars & Counterclockwise Triangles)

(B) Tiling using Nested Four-Pointed Stars (and Nested Squares)

(Clockwise Stars)

(Counterclockwise Stars)

(Clockwise Stars)

(Counterclockwise Stars)

(Type 1: Clockwise Stars & Clockwise Squares)

(Type 2: Clockwise Stars & Counterclockwise Squares)

(Type 3: Counterclockwise Stars & Clockwise Squares)

(Type 4: Counterclockwise Stars & Counterclockwise Squares)

( Mathematical software used: GeoGebra )


Related posts:

• Nested Stars
• Tiling using Nested Stars (1)
• Tiling by Nested Polygons (1)
• Tiling by Nested Polygons (2)
• Tiling using Nested Crosses

Tiling using Nested Crosses

(A) Tiling using Nested Crosses

(Nested Crosses)

(B) Tiling using Nested Crosses and Nested Squares

( Mathematical software used: GeoGebra )


Related posts:

• Tiling by Nested Polygons (1)
• Tiling by Nested Polygons (2)
• Tiling using Nested Stars (1)
• Tiling using Nested Stars (2)
• Tiling using Rounded Crosses