modulo art: computer-based design
TRANSCRIPT
MODULO ART:Computer- Based
Design
LIVIN G. REJUSO
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Mathematics can be considered as a study of patterns . One of the ways in which we use number patterns is in the creation of unique and artistically pleasing designs.
This design from number pattern in Modular Arithmetic formed Modulo Art.
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Modular Arithmetic
modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
12
6
39
12
457
8
10
11
What is the time if you add 5 hours to
11 o’clock? MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
12
6
39
12
457
8
10
11
What is the time if you add 12 hours to
12 o’clock? MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
12
6
39
12
457
8
10
11
9 o’clock + 9 hours?
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
3 1
2
0
12
6
9
4
57
8
10
11
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
3 1
2
0
Modulo= Remainder or Residue
Modulo 4MODULO ART:
Computer- Based DesignBy: LIVIN G. REJUSO
Modular Arithmetic
0 1 2 3123
Modulo 4- Addition
2 3 0
3
0
0
1
1
2
Does it create pattern? MODULO ART:
Computer- Based DesignBy: LIVIN G. REJUSO
0 1 2 3
Modulo 4- Addition
If we make
as our legend……
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 3
If we substitute each legend to our pattern, what happen?
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 2 3 02 3 0 13 0 1 2
Modulo Art Pattern
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Modular Arithmetic
0 1 2 31 1 2 32 2 0 23 3 2 1
Modulo 4- Multiplication
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 3
If we substitute each legend to our pattern, what happen?
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
MODULO ART:Computer- Based Design
0 1 2 31 1 2 32 2 0 23 3 2 1
0 1 2 3
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 3
0 1 2 31 1 2 32 2 0 23 3 2 1
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
0 1 2 31 1 2 32 2 0 23 3 2 1
0 1 2 31 2 3 02 3 0 13 0 1 2
Addition Pattern
Multiplication
Pattern
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Design
0123123023013012
0123123023013012012312302301012
012312302301012
0123112322023321
012311232202332101231123220221
01231123220221MODULO ART:
Computer- Based DesignBy: LIVIN G. REJUSO
Design
012312302301012
012312302301
012
0123 1230 2301 012
0123
1230
2301 01
201231123220221
01231123220221
0123 1123 220221
0123
1123
2202 21
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Design
012312302301012
0123 1230 2301 012
0123 1230 2301 012
01231230230101201231123220221
0123 1123 220221
01231123220221
0123 1123 220221
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
5 TYPES OF MODULO ART1. Grid /Latin square
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
2. Converging segment
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
3. Standard Kaleidoscope
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
4. Circular Kaleidoscope
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
5. Residue Kaleidoscope
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
1. Latin square
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
2. Converging segment/design
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
3. Standard Kaleidoscope
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
4. Circular Kaleidoscope
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO
Thank you so much
MODULO ART:Computer- Based Design
By: LIVIN G. REJUSO