สำนักราชบัณฑิตยสภา

«“√ “√ √“™∫— ≥±‘µ¬ ∂“π ªï ∑’Ë Ú˜ ©∫— ∫∑’Ë Ò ¡.§.-¡’ .§. ÚıÙı ¬ß§å «‘ ¡≈ ‡≈≥∫ÿ √’ Òˆ˘ ‡°≈Á ¥À‘ ¡– √ÿ ª ¡’ ºŸâ π„®»÷ °…“‚§√ß √â “ß∑’Ë ¡’ ‡√¢“§≥‘ µæ√à Õß®”π«πÕ’ °¡“° ‡π◊Ë Õß ®“°‡™◊Ë Õ«à “§«“¡‡¢â “„®∑’Ë ≈÷ °´÷È ß¢Õß∑’Ë ¡“ ¢Õß ¡∫— µ‘ ¥— ß°≈à “« πà “®–𔉪 Ÿ à §«“¡ ‡¢â “„®‡°’Ë ¬«°— ∫°≈«‘ ∏“π‡™‘ ß™’ «¿“æ ·≈–‡™‘ ß°“¬¿“æ¢Õß‚§√ß √â “ß∑’Ë ¡’ ≈— °…≥–‡ªì π‡√¢“§≥‘ µæ√à Õß®”π«π ‡À≈à “π’ È ‰¥â ¥’ ¢÷ È π, √«¡∑— È ß™à «¬„Àâ “¡“√∂ ®— ¥°“√§«∫§ÿ ¡ª√“°Ø°“√≥å ∑’Ë ‡°’Ë ¬« ‡π◊Ë Õß°— π¥â «¬ ¡∫— µ‘ √à «¡∑’Ë ‡√’ ¬°«à “ ‡√¢“§≥‘ µæ√à Õß®”π«π‡À≈à “π’È ‰¥â Õ¬à “ß¡’ ª√– ‘ ∑∏‘ ¿“æ ®÷ ß¡’ π— °«‘ ®— ¬ ∑—Ë «‚≈°∑’Ë æ¬“¬“¡‰¢ªí ≠À“Õ— π≈’È ≈— ∫∑’Ë π” ¡∫— µ‘ ∑“ߧ≥‘ µ»“ µ√å ‰ª„™â ‡ªì 𠂧√ß √⠓ߢÕß√–∫∫µà “ß Ê „π∏√√¡™“µ‘ Õ¬à “ßπà “ª√–À≈“¥‡ªì πÕ¬à “ß¬‘ Ë ß. °‘ µµ‘ °√√¡ª√–°“» ¿“æª√–°Õ∫‡√¢“§≥‘ µæ√à Õß ®”π«π„π∫∑§«“¡π’È §— ¥≈Õ°®“° Àπ— ß ◊ Õ‡√◊Ë Õß Fractal Growth Phe- nomena ¢Õß Tam á s Vicsek Ú . ‡Õ° “√ª√–°Õ∫°“√‡√’ ¬∫‡√’ ¬ß Ò. Mandelbrot BB. The fractal geometry of nature. San Francisco: Freeman; 1982. Ú. Vicsek T. Fractal growth phenomena. 2nd ed. Singapore: Word Scientific Publishing Co; 1992. Û. ÿ ∏“π‘ ∏‘Ï ¬ÿ µ–π— π∑πå , Õÿ ‰√ ®‘ √¡ß§≈°“√, «™‘ √æß»å À«≈∫ÿ µµ“. ‰¡â ¥Õ°· 𠫬. ‰¡â ¥Õ°‰¡â ª√–¥— ∫. °√ÿ ߇∑æœ: ∫√‘ …— ∑ Õ¡√‘ π∑√å æ√‘È πµ‘È ß·Õπ¥å æ— ∫≈‘ ™™‘Ë ß; ÚıÛ¯. Ù. ÿ √‘ π∑√å ¡— ®©‘ ¡™’ æ, ¡ ÿ ¢ ¡— ®©“™’ æ. “√“πÿ °√¡æ◊ ™·≈– — µ«å ‡≈à ¡ Ú. °√ÿ ߇∑æœ: ”π— °æ‘ ¡æå ·æ√à æ‘ ∑¬“; ÚıÛÛ. ı. Briggs J. Fractals: the patterns of chaos. New York: Touchstone Book; 1992. ˆ. Burnie D, ®‘ √π— π∑å æ‘ µ√ª√’ ™“ (ºŸâ ·ª≈). ‰¢ª√‘ »π“∏√√¡™“µ‘ ‡≈à ¡ Ò. °√ÿ ߇∑æœ: ∫√‘ …— ∑ ´’ ‡ÕÁ ¥¬Ÿ ‡§™—Ë π ®”°— ¥ (¡À“™π); ÚıÛ˘. ˜. Glass L, Mackey MC. From clocks to chaos. Princeton Univ Press; 1988. Abstract Fractal Geometry Yongwimol Lenaburi Fellow, the Academy of Science, the Royal Institute, Thailand Many structures or objects found in our surroundings possess special properties known as fractal geometry. The terminology arises from the discovery that these structures have fractal dimen- sions. In this article, only one definition of the dimension of a structure is given together with examples of objects having fractal dimensions, which may be found in nature and are of great interest. Key word : fractal geometry