# Mingjang Chen

Associate Professor

Center for General Education, National Chiao Tung University

Hsinchu, Taiwan

A new method by using Structural Cloning Method (SCM) and Leaping Iterated Function System (LIFS) to explore landscape painting and Illusion are presented in these artworks. SCM is a visual interface to define different combinations of geometry transformations and LIFS is an improved version of Iterated Function System (IFS) within SCM. Instead of exponential growing loading while iterating; LIFS takes only constant computing resources. From the viewpoint of visual design, SCM and LIFS together build a bridge between mathematic and aesthetic, and they then make fractals and landscape paintings more tractable. However, it is much more challenge to convey a natural feeling in such a painting without the feeling of mathematics.

Rising Clouds over Woods

17"x22"

digital print

2010

Using Structural Cloning Method and Leaping Iterated Function System, chaotic patterns, clouds, trees, etc, can be designed easily. This picture is a combination of these chaotic patterns and is compiled on PowerPoint by AMA, an addins for digital content design and presentation.

Flowing Curves

17"x22"

digital print

2010

This artwork is a symmetrical pattern of type P4 with illusion. Its basic pattern is a bipartite graph, and many copies of the pattern are laid over a proper overlapped array.

(1) Complete r-partite graph is a graph, whose vertices can be divided into r disjoint sets, such that for any two vertices in different sets are connected by an edge and vertices in the same set are not connected.

(2) The basic pattern of the work is a complete bipartite graph. The first group of vertices of the complete bipartite graph is positioned on a square, the distance of adjacent vertices are equal, and the second group of vertices of the complete bipartite graph is positioned on an oval.

(3) There are 32 vertices on the first group and there are 24 vertices on this oval. So, there are 32*27 line segments for each basic pattern. The transparency of these line segments is closed to 98%.

An illusion of flowing curves can be found in this art work because of Self-organization and Association Field Effects of human visual system.

(1) Complete r-partite graph is a graph, whose vertices can be divided into r disjoint sets, such that for any two vertices in different sets are connected by an edge and vertices in the same set are not connected.

(2) The basic pattern of the work is a complete bipartite graph. The first group of vertices of the complete bipartite graph is positioned on a square, the distance of adjacent vertices are equal, and the second group of vertices of the complete bipartite graph is positioned on an oval.

(3) There are 32 vertices on the first group and there are 24 vertices on this oval. So, there are 32*27 line segments for each basic pattern. The transparency of these line segments is closed to 98%.

An illusion of flowing curves can be found in this art work because of Self-organization and Association Field Effects of human visual system.