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Matematični pristopi pri oblikovanju tekstilnih površin
Puc, Sabina (Author), Škrekovski, Riste (Mentor) More about this mentor... This link opens in a new window

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Abstract
V raziskavi je predstavljen interdisciplinarni kreativni postopek oblikovanja ploskovnih vzorcev z matematičnimi funkcijami dveh spremenljivk. Na podlagi zasnovanih matematičnih enačb z linearnimi kombinacijami potenc sinusne funkcije smo z računalniškim algebrskim sistemom Wolfram Mathematica generirali trirazsežne grafe, ki smo jih presekali z izbranim številom k vodoravnih ravnin xy na enakomerno ali neenakomerno razmaknjenih nivojih. Dobljene preseke smo projicirali na ravnino z = 0, kjer so nastale ravninske disjunktne unije točkovnic. Z digitalnim prevodom abstraktnih matematičnih zapisov v vizualni medij smo dosegli nazorne vizualne podobe, ki smo jim v ustvarjalnem procesu postavili estetske zahteve. Kriteriji so obsegali likovni potencial periodične konfiguracije, izraznost prvin strukturnih gradnikov in skladnost odnosov v kompoziciji. V nadaljevanju smo ustreznim ravninskim disjunktnim unijam točkovnic z opcionalnimi parametri definirali barvne kombinacije za območja med točkovnicami in grafične atribute konturnih linij, s čimer smo ustvarili enoplastne ploskovne vzorce. Kompozicijsko raznovrstnost smo še povečali z medsebojnim nalaganjem in prekrivanjem različnega števila plasti, ki smo jih s sestavljanjem združili v večplastne konfiguracije. Rezultat raziskovalnega dela je oblikovana matematična kolekcije digitalnih vzorcev, v katero so vključeni enoplastni in večplastni ploskovni vzorci. S sistematično strukturno analizo smo referenčnim površinam vzorcev določili pripadajoče tapetne grupe na podlagi ploskovne organizacije, urejenosti modularnih strukturnih gradnikov in simetrijskih operacij. Realizirali smo tudi digitalno kolekcijo periodičnih vzorcev na osnovi 17 tapetnih grup, kjer smo iz nesimetrične celice izbranega ploskovnega vzorca, skladno z značilnostjo posamezne tapetne grupe, izvedli ustrezne simetrijske operacije in dobljeno simetrično jedrno enoto motiva, s ponavljanjem v pravilnih intervalih, nanizali z vzporednimi premiki znotraj elementarne mrežne strukture. V zaključku smo v galeriji Zeta v ospredje postavili likovno interakcijo gledalca z digitalnimi površinami ploskovnih vzorcev brez zapisa matematičnega ozadja.

Language:Slovenian
Keywords:ploskovni vzorci, algebrski sistem Wolfram Mathematica, nivojnice, ravninske disjunktne unije točkovnic, simetrija, tapetne grupe
Work type:Doctoral dissertation (mb31)
Organization:NTF - Faculty of Natural Sciences and Engineering
Year:2019
Views:375
Downloads:247
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Secondary language

Language:English
Title:Mathematical approaches in the design of textile surfaces
Abstract:
This research focuses on the creative interdisciplinary process of designing repetitive patterns stemming from periodic functions with two variables. By using Wolfram Mathematica, a computer algebra system, we generated 3D-graphs based on pre-set mathematical functions with linear combination of powers of sinusoidal functions. The latter were then cut by a selected number k on the horizontal xy plane on equal or unequal levels. The cuts were projected onto plane z = 0, where contour maps appeared. With a digital translation of abstract mathematical values onto a visual media, a visual image based on aesthetic concepts was created. The creative criteria were based on the artistic potential of periodic configurations, expressive properties of structural units and the congruence of various compositions. Colour combinations and contour lines were then applied to corresponding contour maps by means of optional parameters, thus creating one-layered repetitive patterns. An even greater diversity of composition was achieved by layering and combining planes into multi-layered configurations. Since the result of this research was to design a mathematical collection with one- and multi-layered repetitive digital patterns, a systematic structural analysis allowed us to define wallpaper groups based on planar distribution, disposition of modular structure units and symmetric operations. A digital collection of periodical patterns based on seventeen wallpaper groups was also created, in which symmetric operations were applied onto an asymmetric cell of a selected repetitive pattern in accordance with the characteristics of the various wallpaper groups. The symmetric unit of one motif which repeats itself in regular intervals was then applied in parallel rows within the elementary grid. Finally, we put up an exhibition at Zeta Gallery, where we focused on the artistic impact which the repetitive patterns, devoid of mathematical groundwork, had on visitors.

Keywords:repetitive patterns, computer algebra system Wolfram Mathematica, contour line, contour map, symmetry, wallpaper group

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