Graphics using Abstract Algebra

[zak100]

Homework Statement

I can't understand how abstract aljebra helps in creating graphical patterns. I don't find eq related to Groups. Do we consider predefined structures [/B]

Homework Equations

No equation only patterns. one pattern is attached

The Attempt at a Solution

I don't know how it works so no attempt to solution. But i have some idea which i want to share. For the attached fig, we can have 2 images. One is the white horseman & the other is a brown horseman. i think its a binary pattern. When we get the value '1' for a operation O1 then we display brown horse man otherwise we display white horse man if we get a value '0'.

Some body please guide me.

Zulfi.

 

[pasmith]

What is the question actually asking you to do?

Do you understand that the operations (translations, rotations, reflections) which preserve the pattern form a group?

 

[MidgetDwarf]

Homework Statement

I can't understand how abstract aljebra helps in creating graphical patterns. I don't find eq related to Groups. Do we consider predefined structures [/B]

Homework Equations

No equation only patterns. one pattern is attached

The Attempt at a Solution

I don't know how it works so no attempt to solution. But i have some idea which i want to share. For the attached fig, we can have 2 images. One is the white horseman & the other is a brown horseman. i think its a binary pattern. When we get the value '1' for a operation O1 then we display brown horse man otherwise we display white horse man if we get a value '0'.

Some body please guide me.

Zulfi.

Maybe try reading about the group of all rigid motions.

 

[MidgetDwarf]

Maybe try reading about the group of rigid motions. It requires a bit of group theory and linear algebra, so you have to specify the level you are at for an appropriate answer.

 

[haruspex]

Try looking up tessellations and wallpaper groups.