Here you can see artworks and sculptures in which mathematical laws were posed as basis. Artworks by M.C. Escher and his followers.

## Wednesday, December 24, 2008

### Kinetic sculptures by Haruki Nakamura

## Sunday, October 19, 2008

### Fibonacci spiral in nature

Fibonacci tiling | Fibonacci spiral |

You can see Fibonacci spiral even in shapes of galaxies. Although Nautilus shell looks very similar to Fibinacci spiral, it does not. Ivars Peterson in his article Sea Shell Spirals proved this fact. Nevertheless, Nautilus shell is one of examples of fractals in nature.

## Sunday, October 12, 2008

### Fractal tilings

## Wednesday, September 24, 2008

### Abstract creations by Vladimir Bulatov

## Sunday, July 6, 2008

### Tessellations of David Bailey

One of them is artist from England

**David Bailey**. He creates his images in pen and watercolour.

The main motifs of his tessellations are birds.

The more complex constructions come in, when two distinct motifs are used in conjunction with each other.

Besides usual animals David Bailey uses imaginary creatures to create his wonderful artworks. Below you can see dinosaur-like creatures. The main distinguishing feature of this drawing is that only part of the image was used for animals, when other space shows only borders of elementary tiles. It helps to better understand, which kind of symmetry was used in every case.

Also he created several artworks, which reminds Escher's artworks with mutable tessellations like *Metamorphoses*. The image below shows the same process as in Escher's lithograph *Development I*. But David Bailey used birds as motif for his artwork instead of Escher's lizards.

The reverse process is shown in the image below.

More images by David Bailey you see at his personal site http://www.tess-elation.co.uk/. Besides this you you read some articles about tessellation art and Escher's artworks.

## Sunday, June 22, 2008

### Fractal waves

*36 Views of Mount Fuji.*It depicts an enormous wave threatening boats near the Japanese prefecture of Kanagawa; Mount Fuji can be seen in the background. The main reason of publishing this artwork here is highly detailed painted wave. As we know, some artworks, which are close to fractal images by detailed elaboration, were created long before the inventing fractals by Benoît Mandelbrot. Sea waves can be represented by many types of fractals, as you can see below.

Also, a wave with horses figures are depicted on the cover of English rock group Keane "Under The Iron Sea" (2006).

## Wednesday, April 30, 2008

### Menger sponge

Like the Sierpinski carpet begins from square, Menger sponge begins from cube. Every face of the cube is divided into 9 smaller squares. This operation divide the cube into 27 smaller cubes. Then center cubes from all faces and the inner center cube are removed, leaving 20. This is a level 1 Menger Sponge. The next levels forms by repeating these steps to all 20 cubes rest. Below you can see first four levels.

Below you can see the Menger sponge with cut off corner, which was designed by Seb Przd.

There's also similar three-dimensional fractal based on tetrahedron, which is a generalization of the Sierpinski triangle into three dimensions. Below, you can see two versions of the Sierpinski pyramid and the Menger sponge in a single image.

## Saturday, April 26, 2008

## Friday, April 18, 2008

### Sierpinski carpet

**Andrew Pike**. It reminds us zoomed newspaper photos, when we can see particular dots of various size. But it's unusual image, because every element in it is not a simple dot, but one of several generations of the

*Sierpinski carpet*fractal, which was first described by

**Wacław Sierpiński**in

**1916**.

Andrew Pike used two series of several generations of the fractal. The one series began from the black color, and another from white. He designed a computer program, which divided a photo of Wacław Sierpiński into squares of various values of grey color. To avoid strong color changing he used dithering technique.

So, the inventor of the fractal was pictured with his fractal.

*Sierpinski carpet*is a two dimensional generalization of the one dimensional fractal

*Cantor dust*. Also, there's generalization of the

*Sierpinski carpet*into three dimensions, which named

*Menger sponge*.

## Friday, April 11, 2008

### Escher's favorite building

## Thursday, March 20, 2008

### Wood work by Hans de Koning

**Hans de Koning**(see above). The shapes of the most of his works are based on impossible figures. His works are flat, but he uses different kinds of wood to make three-dimensional effect. Wood planks with different hues imitate sides slope and opacity of the impossible figure.

## Saturday, March 1, 2008

### Fractal trees

**fractal trees**, which are consist of lines and curves.

The rainbow fractal Julius tree below was crated with help of the computer program Fractal Imaginator. The tree reminds rounded Pythagoras tree, where squares were replaced to thin rectangles. The tree fractal can be created not only with help of straight lines or rectangles, but also with help of curves and spirals. Below, you can see a title for the High School Course "Gödel, Escher, Bach: A Mental Space Odyssey" by Justin Curry and Curran Kelleher, where curved fractal tree is used. The spiral was chosen as base element for this fractal, which gives many elegant curls.

## Monday, February 18, 2008

### Hilbert curve

**Hilbert curve**is a continuous fractal space filling curve, which was first described by German mathematician David Hilbert in 1891. Below you can see 5 first steps of the plane Hilbert curve.

But the Hilbert curve looks more interesting if it represent in three dimensions. Carlo H. Séquin, a professor of Berkley, created a small 5" metal sculpture of Hilbert curve, which he called "Hilbert 512". You can see it below.

It was also be modeled by Torolf Sauermann in the program Maxwell renderer. Below, you can see the second step of the three-dimensional Hilbert curve and two versions of cubic Hilbert curve.