Yojic Matrix(Scramble)

What is the Yojic Matrix?

Yojic idea was developed as some sort of sliding puzzle around in 2008.
There are colored tiles arranged in a matrix that you can move.
The puzzle name is Yojic Matrix.
It is a kind of simple sliding puzzle.
The next few are typical Yojic Matrix.

Ring 3

Ring 4

Yojic 4

Yojic 5

Yojic 6

Yojic 3


How to play


First push 'Play' button and it will begin.
The small image is your target goal.
You should make the main pattern to the same one.
If you touch a center square(hexagon), you can move the squares(hexagons) around the center.
The center square(hexagon) must be surrounded eight squares(six hexagons).

Touch right side of the center piece : clockwise
Touch left side of the center piece : counterclockwise


In the puzzle, some are easy to get answer, but some are quite difficult.
To get enough to enjoy, it is recommended that you learn the movement of the basic.

Basic some movements

[Square type Yojic]
When red blue yellow make a round, tiles 1,2,3,4,5,6,7,8,9 get movement, such as the following.


for example



[Hexagon type Yojic]
When red blue yellow make a round, tiles 1,2,3,4,5,6,7 get the following movement.

In addition, your thinking is required in order to obtain an better answer,
please create a variety of your own techniques.

To get answer to hard questions needs to try many different arrangements as possible.
So, such round is effective for makeing various permutations.


Although Yoji3, Yojic4 are basic in th Yojic Marix, there are also bigger ones
These are bigger Yojic Matrix.

Yojic Matrix S140

Yojic Matrix H68

Of course you can play with it.
First, push 'Play' button and it will begin.
How to play is the same as the basic Yojic Matrix.


For art

First, take a look at Color Diffusion.

Color Diffusion

This is 100 * 70 Yojic Matrix. This is color diffusion.
The Yojic Matrix method is used to express color diffusion.
This apllication expresses color diffusion.
To tell the truth,when I was drawing a painting on a computer,
I needed to create a new way how to blur the painting soft
without changing the number of each color of pixels.
To create a matrix of pixels tailored to the size of the screen, using so many random numbers,
it is the idea to specify a large amount of coordinates, rotate the pixels around the center of the designated pixel by random coordinate.

This is beginning of the yojic matrix idea.


And, also maybe "the idea will make interesting puzzles." I thought.

diffusion

Cloth like

Blurring dog

trees

I am using the Yojic idea for my digital art.
I made a big Yojic, about 1000*1000 matrix.
One pixel is one element(piece) of the yojic matrix.
That yojic can make diffusion expression of colors.



last Yojic

Small but especially difficult Yojic Matrix

Last Yojic S

Last Yojic H

The smallest square type and the smallest hexagon type are presented here.
The most basic, but the most difficult.
However, these are particularly hard Yojic Matrixs.<br> There are 16 questions each, but most are too difficult and require the power of a computer.
If you are interested in computer programming, think about algorithms and try programming.
How about using AI as a method? Please try

br>

etc.

Anyway, I think Yojic Matrix can be algebraic nice model,
It is a pure algebra world on an algebraic geometory.
I'm really interested in finite replacement groups of Yojic matrix.
There are so many forms, so many sizes.
Some are easy, Some are not easy.
It may be interesting to think about the Yojic way on various manifolds.
How about the Yojic on a dodecahedron?
How about the yojic on a torus?
Do you know right dice and left dice?
Right dice is obiously impossible to get left dice with Yojic transformation.
And
Rubik's Cube is a kind of subgroup of Yojic Matrix with Rubik's condition on a cube.
I want to leave te yojic idea to experts

I just want to say "if you are fiery algebraical researcher.
Please, sometimes, take a break and enjoy the Yojic Puzzle."
You know. Poincare conjecture has finished.
Especially, Knot Theory?
ha! ha! ha! ...


Home


In addition, at the thought of another,
When considering movement of elementary particles, the surface exposed to the electron wave, might be able to express the movement of the particles occur there.
When sunlight hits the thing? , When the X-ray hits the film?
Solar panels How?
Kamiokande? Particle around which neutrinos pass through or to what kind of movement?
When a particle hits, or when it passes, the particles around the passing point or to what kind of movement?

Knights

Home

Five knights

Ten knights

Cat Knights


It's not a Yojic puzzle, but I made an original (by Y.H 2021.April) puzzle, so I will provide it at the end.
I tried to make the movement of the chess knight into a puzzle.
Please feel free to enjoy it.
Move the each knight and making the same arrangement as target is completed.
Some are difficult and some are easy.
Click the knight to select it and move it according to the movement of the knight.
The trick is to evacuate the disturbing knight and move the target knight.
Five Knights, Ten Knights, Ten cat knights.
The last Ten Cat Knights was made as a demonstration. Please refer.



And two puzzles

Arrange inorder and Matching

Arrange in order

Matching

Some Magic squares


There are some Magic squares making from Euler squares.

Magic Square