OPTIMIZACIJA

1. http://mathdl.maa.org/images/upload_library/22/Evans/Horizons-Feb06-p.06-09.pdfhttp://mathdl.maa.org/images/upload_library/22/Evans/Horizons-Feb06-p.06-09.pdf OPTIMIZACIJA I UMJETNOST

2. Robert Bosch – matematičar i umjetnik

3. Georges Seurat: Nedjeljno poslijepodne na otoku Le Grande Jatte, 1884 - 6

4. Leon Harmon: Predsjednik Lincoln, 1973. Salvador Dali: Gala kontemplira nad Mediteranom, 1976.

5. Mona Lisa, prvi pokušaj, 2001. 3 seta domina

6. Mona Lisa, 40 kompleta domina

13. Robert Bosch, Zagrljaj, 2010. Robert Bosch, Vanjski prsten

14. Robert Bosch, Sfera i labirint, 2011.

16. our task is to place our task is to place s s sets of double-nine dominoes on the can- sets of double-nine dominoes on the can- vas—with each domino positioned either horizontally or ver- vas—with each domino positioned either horizontally or ver- tically, covering precisely two squares of the canvas—in such tically, covering precisely two squares of the canvas—in such a way that the resulting arrangement resembles the target a way that the resulting arrangement resembles the target image as closely as possible. image as closely as possible. Note that in place of a set of building-block photographs Note that in place of a set of building-block photographs F F , , , , we have a set of double-nine dominoes we have a set of double-nine dominoes D D = { = { d d = ( = ( d d d d ) : 0 ) : 0 ≤ ≤ 1 1 2 2 s s d d ≤ ≤ d d ≤9} ≤9} , and we need to use each domino , and we need to use each domino d d ∈ ∈ D D exactly exactly 1 1 2 2 d d , , d d times. Since domino times. Since domino = ( = ( d d ) is black and has ) is black and has d d white dots white dots 1 1 2 2 1 1 painted on one square and painted on one square and d d white dots painted on the other, white dots painted on the other, 2 2 our task is to place s ets of double-nine dominoes on the can- vas—with each domino positioned either horizontally or ver- tically, covering precisely two squares of the canvas—in such a way that the resulting arrangement resembles the target image as closely as possible. Note that in place of a set of building-block photographs F, e have a set of double-nine dominoes D= {d= (d1, d2) : 0 ≤d1≤ d2≤9}, and we need to use each domino d∈D exactly stimes. Since domino d= (d1, d2) is black and has d1 white dotspainted on one square and d2 white dots painted on the other, domino d= (d1, d2) can be thought of as a domino-shaped photograph, half of which has brightness d1 and half of which has brightness d2, with both brightness values measured on a 0-to-9, black-to-white scale. Also note that since there are 55 dominoes per set, we need to make sure that when we partition the target image and canvas into m rows and n columns of congruent squares, m and n satisfy mn = 110 s . The portrait in Figure 2 has m = 33, n = 30, and s = 9. Finally, note that it is convenient here to denote the brightness of the row- i -column- j square of our target image b domino domino d d = ( = ( d d , , d d ) can be thought of as a domino-shaped ) can be thought of as a domino-shaped 1 1 2 2 photograph, half of which has brightness photograph, half of which has brightness d d and half of which and half of which 1 1 has brightness has brightness d d , with both brightness values measured on a , with both brightness values measured on a 2 2 0-to-9, black-to-white scale. 0-to-9, black-to-white scale. Also note that since there are 55 dominoes per set, we need Also note that since there are 55 dominoes per set, we need to make sure that when we partition the target image and to make sure that when we partition the target image and n n columns of congruent squares, columns of congruent squares, canvas into canvas into m m rows and rows and m m and and n n satisfy satisfy mn mn = 110 = 110 s s . The portrait in Figure 2 has . The portrait in Figure 2 has m m = 33, = 33, s s n n = 30, and = 30, and = 9. = 9. Finally, note that it is convenient here to denote the Finally, note that it is convenient here to denote the brigh brigh