I have trouble editting the HTML for the blog...
I just can classify them here...
Feb-M.C escher research
Mar-culture research
Api-cutlture research
May-design
Saturday, May 16, 2009
Tuesday, May 12, 2009
design_hero
I try to make complex shape.this is a hero who wear their traditional cloth.
the idea is from the right side of the picture.
I think I can emphasize the detail in the cloth later and make it more believable.
the idea is from the right side of the picture.
I think I can emphasize the detail in the cloth later and make it more believable.
Tessellations by Recognizable Figures
All of Escher’s tessellations by recognizable figures are derived from just a handful of geometric patterns. There are several different techniques that Escher used, and sometimes he combined techniques as well, but all involve a transformation from a simple geometric pattern to a complicated, recognizable figure.
The simplest example of an Escher tessellation is based on a square. Start with a simple geometric pattern, a square grid, and then change that ever so slightly.
What do you see? Some will think it looks like interlocked men, others may see birds. Decorating each of the newly formed tiles can emphasize a particular interpretation, and creates a tessellation by recognizable figures, in the style of Escher.
I think this is very interesting. Escher's idea is exactly animation morphing process.
The simplest example of an Escher tessellation is based on a square. Start with a simple geometric pattern, a square grid, and then change that ever so slightly.
What do you see? Some will think it looks like interlocked men, others may see birds. Decorating each of the newly formed tiles can emphasize a particular interpretation, and creates a tessellation by recognizable figures, in the style of Escher.
I think this is very interesting. Escher's idea is exactly animation morphing process.
Monday, May 11, 2009
Convex Polygons
Every shape of triangle can be used to tessellate the plane. Every shape of quadrilateral can be used to tessellate the plane. In both cases, the angle sum of the shape plays a key role. Since triangles have angle sum 180° and quadrilaterals have angle sum 360°, copies of one tile can fill out the 360° surrounding a vertex of the tessellation.
The next simplest shape after the three and four sided polygon is the five sided polygon: the pentagon. The angle sum of any pentagon is 540°, because we can divide the pentagon into three triangles:
Unlike the triangle and quadrilateral case, the pentagon's angle sum of 540° is not helpful when trying to fit a bunch of pentagons around a vertex. In fact, there are pentagons which do not tessellate the plane.
some are not working:
some are working
Non-Euclidean Geometry:
The next simplest shape after the three and four sided polygon is the five sided polygon: the pentagon. The angle sum of any pentagon is 540°, because we can divide the pentagon into three triangles:
Unlike the triangle and quadrilateral case, the pentagon's angle sum of 540° is not helpful when trying to fit a bunch of pentagons around a vertex. In fact, there are pentagons which do not tessellate the plane.
some are not working:
some are working
Non-Euclidean Geometry:
design_fish(Tessellations)
I try to put the fish image which I made before by the Tessellations math.
Tessellations by Polygons
The picture works because all three corners (A, B, and C) of the triangle come together to make a 180° angle - a straight line. This property of triangles will be the foundation of our study of polygon tessellations
Sunday, May 10, 2009
Math and the Art of MC Escher
I am reading the online book of Math and the Art of MC Escher.http://math.slu.edu/escher/index.php/Main_Page
there are some topic which help me a lot.(I will keep to post)
Tessellations:
A tessellation is a covering of the plane by shapes, called tiles, so that there are no empty spaces and no overlapped tiles. Tessellations are also called tilings.Some tessellations involve many types of tiles, but the most interesting tessellations use only one or a few different tiles to fill the plane. If the tiles are regular polygons (all sides are congruent and all angles are congruent) and vertices only meet vertices we say that the tessellation is a regular tessellation.An example of tessellations using only a few different tiles are the semi-regular tessellations. These tessellations are made up of two or more types of regular polygons, vertices only meet vertices and the configuration around every vertex is the same.
Escher lays out his methods for creating tessellations:
1.Begin with a tessellation by geometric shapes.
2."Mold the form". Here, he bends and manipulates the straight lines of the geometric scaffolding.
3.Look at the resulting pattern and attempt to recognize a figure.
4.Push the pattern towards the desired shape.
there are some topic which help me a lot.(I will keep to post)
Tessellations:
A tessellation is a covering of the plane by shapes, called tiles, so that there are no empty spaces and no overlapped tiles. Tessellations are also called tilings.Some tessellations involve many types of tiles, but the most interesting tessellations use only one or a few different tiles to fill the plane. If the tiles are regular polygons (all sides are congruent and all angles are congruent) and vertices only meet vertices we say that the tessellation is a regular tessellation.An example of tessellations using only a few different tiles are the semi-regular tessellations. These tessellations are made up of two or more types of regular polygons, vertices only meet vertices and the configuration around every vertex is the same.
Escher lays out his methods for creating tessellations:
1.Begin with a tessellation by geometric shapes.
2."Mold the form". Here, he bends and manipulates the straight lines of the geometric scaffolding.
3.Look at the resulting pattern and attempt to recognize a figure.
4.Push the pattern towards the desired shape.
a interview from escher
just see a interview from M.C escher.
the idea of all the architecture is interesting.
Subscribe to:
Posts (Atom)