MODULO ART

MODULO ARITHMETICMODULO ARITHMETIC

ADDITION

0 1 2 30 0 1 2 3

1 1 2 3 0

2 2 3 0 1

3 3 0 1 2

MODULO 4 MODULO 70 1 2 3 4 5 6

0 0 1 2 3 4 5 6

1 1 2 3 4 5 6 0

2 2 3 4 5 6 0 1

3 3 4 5 6 0 1 2

4 4 5 6 0 1 2 3

5 5 6 0 1 2 3 4

6 6 0 1 2 3 4 5

SUBTRACTIONMODULO 5

0 1 2 3 4

0 0 4 3 2 1

1 1 0 4 3 2

2 2 1 0 4 3

3 3 2 1 0 4

4 4 3 2 1 0

MODULO 80 1 2 3 4 5 6 7

0 0 7 6 5 4 3 2 1

1 1 0 7 6 5 4 3 2

2 2 1 0 7 6 5 4 3

3 3 2 1 0 7 6 5 4

4 4 3 2 1 0 7 6 5

5 5 4 3 2 1 0 7 6

6 6 5 4 3 2 1 0 7

7 7 6 5 4 3 2 1 0

MULTIPLICATIONMODULO 5MODULO 7

0 1 2 3 4 5 6

0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6

2 0 2 4 6 1 3 5

3 0 3 6 2 5 1 4

4 0 4 1 5 2 6 3

5 0 5 3 1 6 4 2

6 0 6 5 4 3 2 1

LATIN SQUARE

CONVERGING SEGMENT

STANDARD KALEIDOSCOPE

CIRCULAR KALEIDOSCOPE

CIRCULAR RESIDUE

LATIN SQUARE

10 32

0

0

0 1

1

1

2

2

2

3

3

3

3

2

1

0

LATIN SQUARE

10 32

0

0

0 1

1

1

2

2

2

3

3

3

3

2

1

0

10 32

0

0

0 1

1

1

2

2

2

3

3

3

REPETITION

10 32

0

0

0 1

1

1

2

2

2

3

3

3

10 32

0

0

0 1

1

1

2

2

2

3

3

3

10 32

0

0

0 1

1

1

2

2

2

3

3

3

HOME

10 32

0

0

0 1

1

1

2

2

2

3

3

3

ROTATION1

03

2

0

0

01

1

1

2

2

23

3

3

1 03 2

0

0

01

1

1

2

2

2

3

3

3

10

32

0

0

01

1

1

2

2

2 3

3

3

10 32

0

0

0 1

1

1

2

2

2

3

3

3

REFLECTION

1 03 2

0

0

01

1

1

2

2

2

3

3

3

10 32

0

0

0 1

1

1

2

2

2

3

3

3

1 03 2

0

0

01

1

1

2

2

2

3

3

3

HOME

0 1 2 3

1 2 3

2 3 1

3 0 1 2

0

0

0 1 2 3

1 2 3

2 3 1

3 0 1 2

0

0

0

1

2

3

home

CIRCULAR KALEIDOSCOPE

2

2

2 11

1

1

23

3 3

3

4

4

4

4 1

2

3

4

2

2

2

1

123

3 3

3

4

4

4

4 1

2

3

4

1

2

2

2

1 123

3

3

4

4

4

1

2

3

4

1

2

2

1 123

3

3

4

4

4

1

2

3

4

1

2

2

1 123

3

3

4

4

4

1

2

3

4

1

2

2

1 123

3

3

4

4

4

1

2

3

4

1

2

2

1 123

3

4

4

4

1

2

3

4

1

2

2

123

3

4

4

1

2

3

4

1

2

2

123

3

4

4

1

2

3

4

1

2

2

123

3

4

4

1

2

3

4

1

REFLECTION

ROTATION

home

x 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

mod 19 9 18 8 17 7 16 6 15 5 14 4 13 3 12 2 11 1 10

1

3

2

6

4

8

7

1011

9

13

12

15

16

14

1817

5

1

3

2

6

4

8

7

1011

9

13

12

15

16

14

1817

5

1

3

2

6

4

8

7

1011

9

13

12

15

16

14

1817

5

home

00

1122 33

1122

3300

223300

11

330011

22

00 1122

33

1122

3300

223300

11

330011

22

001122

33

1122

3300

223300

11

330011

22

00

112233

1122

3300

223300

11

330011

22

00

1122 33

112233

00

2233 00

11

330011 22

00

1122 33

112233

00

2233 00

11

330011 22

0

0 1

0 1

2

0 1

2

3

0 1

2

3

0 1

2

3

0 1

2

3

0 1

2

3

REFLECTION

ROTATION

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