Fractals by Manny Lorenzo

Some time ago I've published one fractal by Manny Lorenzo in the post about Pythagoras trees. Today I would like to show some his fractals.

Let start from new kinds of Pythagoras trees. He created a tree with spheres and a very strange kind of Pythagoras tree, which has infinity symbol as a base part of fractal. It looks unlike Pythagoras tree, but it is true.

Also he created a set of wonderful fractals of Nautilus shells. Nautilus shell is one of known examples of fractals in nature. 

Except these ones he created another fractal shells.
Visit Manny's Flickr phostostream to see more beatiful fractals.

Escher-like mosaics

M.C. Escher is well known by his artistic regular plane divisions and artworks of impossible constructions. But he also created several artworks with irregular mosaics, which consist of shapes of various animals. Two of them you can see below. As you can see every animal in mosaics are fit all its neighbours without any gaps.

Today may artists follow the way of Escher in creating complex mosaics. Images of Bobby Bogl are worthy, which you can see below. Take a notice of how all parts of his images accurate match to each other.

Kinetic sculptures by Haruki Nakamura

Look at the photo a heart sculpture above, which is consists of closely interconnected gears. Although it seems that gears cannot move it is not. All of them can rotate around their respective centers, which your can see on a video below. Moving of gears are shown approximately on 50th second of the video but it's 

This kind of sculptures are called kinetic because all parts of them can move. It was created by Japanese engineer Haruki Nakamura and represented in 2005 with title Gear's Heart. Unfortunately, there's no any more information about him in the Internet except several images of his sculptures and few videos.

Also he created similar sculpture of cube, which you can see below.

Fibonacci spiral in nature

Fibonacci spiral is a line, which is created by drawing arcs connecting the oppposite corners of the squares in Fibonacci tiling, which is constructed of squares whose sides are successive Fibonacci numbers in length.

Fibonacci tiling

Fibonacci spiral

Fibonacci spiral exists in many objects of wildlife. It's one ob the basic curve, which you can see in small shells of nautilus and even in spirals of galaxies.

Arrangement of seeds in sunflower is an example of Fibonacci spiral among plants.

Hurricane is one of the most destructive power on Earth.

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.

Fibonacci spiral inspired some artist to use it in their artworks. Below you can see an artwork by Petar Milivojevic named Gaia's gift.

Fractal tilings

Fractal shapes can be used as tiles for filling plane. In most cases variations of the Koch snowlake are used. A simple Koch snowflake is represented to the right. To create a set of tiles, which can be used for filling whole plane, we need another variations of the snowlake which exactly match to all convexes and concaves of the first figure.

Two variations of such kind of tilings were represented on Briges 2008 conference, which took place in Leeuwarden (Holland). Both were realized in wood. We see that several kinds of fractal tiles were used in both cases. 

Koch tiling by Edmund Harris

Pentagonal Koch tiling by Chaim Goodman-Strauss

Images were found in Briges 2008 - Leeuwarden pool at Flickr.

More mathematical issues about fractal tiles you can read in the article about Rauzy fractal.