"Perpetual Growth", 9.5'x3', 2011
I spent the past week-and-a-half painting a new mural at Palette Contemporary Art & Craft Gallery in Albuquerque, New Mexico. My goal was to build a non-traditional-format landscape based-upon the Golden Section, an ancient compositional tool used most notably by Renaissance painters and early adopters of Cubism. At nearly ten feet tall, it took me most of the entire first day to work-out the math for the composition of the under-painting. - North
Now some information on how I attained the composition:
Fibonacci numbers and Phi are related to spiral growth.
If you sum the squares of any series of Fibonacci numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral seen in everything from sea shells to galaxies:12 + 12 + 22 + 32 + 52 = 5 x 8
12 + 12 + . . . + F(n)2 = F(n) x F(n+1)
The Golden Section is a ratio based on phi.
The Golden Section is also known as the Golden Mean, Golden Ratio and Divine Proportion. It is a ratio or proportion defined by the number Phi (1.618….)
This ratio has been used by mankind for centuries. Its use may have started as early as with the Egyptians in the design of the pyramids. The Greeks recognized it as
"dividing a line in the extreme and mean ratio" and used it for beauty and balance in the design of architecture. The Renaissance artists knew it as the Divine Proportion and used it for beauty and balance in the design of art. It was used in the design of Notre Dame in Paris and continues today in many examples of art, architecture and design.
"Patchwork: ""Kutoka kwa Utafiti wa Sanaa ya Kale"" - Picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha." "Lengo lake lilikuwa kujenga mandhari isiyo ya kawaida, kulingana na ""Golden Section,"" chombo cha kale cha uundaji kilichotumiwa hasa na wachoraji wa Renaissance na waanzilishi wa mapema wa Kubism." Kwa urefu wa karibu mita tatu, ilinichukua karibu siku nzima ya kwanza kufanya hesabu kwa ajili ya muundo wa chini ya uchoraji. - Kaskazini Sasa baadhi ya habari juu ya jinsi mimi kupatikana muundo: Nambari Fibonacci na Phi ni kuhusiana na ukuaji spiral. Ikiwa utaongeza mraba wa safu yoyote ya nambari za Fibonacci, zitakuwa sawa na nambari ya mwisho ya Fibonacci iliyotumiwa katika safu mara nambari ya Fibonacci inayofuata. Mzunguko wa Fibonacci unaonekana katika kila kitu kutoka kwa makombora ya bahari hadi galaksi: 12 + 12 + 22 + 32 + 52 = 5 x 8 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 . . F (n) = F (n) x F (n + 1) Sehemu ya Dhahabu ni uwiano kulingana na phi. Sehemu ya Dhahabu pia inajulikana kama Golden Mean, Golden Ratio na Divine Proportion. Ni uwiano au uwiano uliofafanuliwa na idadi Phi (1.618....) Kiwango hicho kimetumiwa na wanadamu kwa karne nyingi. Huenda matumizi yake yalianza mapema sana na Wamisri katika kubuni piramidi. Wagiriki waliona kwamba mstari huo uligawanya mstari katika uwiano wa kati na wa mbali, na waliutumia kwa ajili ya urembo na usawaziko katika usanifu wa majengo. Wasanii wa Renaissance walijua kama uwiano wa kimungu na kuitumia kwa uzuri na usawa katika kubuni sanaa. Pia ilitumiwa katika Notre Dame ya Paris na inaendelea leo katika mifano mingi ya sanaa, usanifu na kubuni.