Dinamički modeli filotaksije

master's thesis

• Title (english): Dynamical models of phyllotaxis
• Author: Ivor Madžar
• Mentor: Matko Glunčić (mentor)
• Committee member: Matko Glunčić (predsjednik povjerenstva)
• Committee member: Gorjana Jerbić-Zorc (član povjerenstva)
• Committee member: Mario Novak (član povjerenstva)
• Committee member: Damir Veža (član povjerenstva)
• Committee member: Maja Planinić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2016-09-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Filotaksični uzorci javljaju se kod vaskularnih biljaka kada biljka na rastućem vrhu stvara niz sličnih botaničkih elemenata, kao što su listovi, sjemenke, latice ili ljuske. Najčešći ovakav uzorak je onaj u kojem su elementi organizirani u dvije obitelji spirala koje se rotiraju u suprotnim smjerovima. Broj spirala u svakoj od ovih ovitelji su uzastopni brojevi Fibonaccijeva niza u kojem je svaki član suma prethodna dva. U ovom istraživanju razviti ću teorijski dinamički model koji uključuje vremensku evoluciju filotaksičnog uzorka. Pomoću modela pokušati ću odgovoriti na sljedeća fundamentalna pitanja: Zašto je između svih mogućih regularnih spiralnih uzoraka, Fibonaccijeva spirala favorizirana? Koji su ostali uzorci teorijski mogući, te koji su mehanizmi tranzicije između različitih uzoraka?

Abstract (english)

Phyllotaxic patters are generated whenever a vascular plant on its apex produces similar botanical elements like leaves, seeds, florets or shells. The most common pattern is the one in which the elements are organized in two spiral families which rotate in opposite directions. Number of spirals in each of those two families are successive numbers of Fibonacci series in which each number is the sum of the two previous ones. In this research I will develop a theoretical dynamical model which includes time evolution of a phyllotactic pattern. With this model I will try to answer these fundamental questions: Why is, among the all possible general spiral patterns, the one by Fibonacci most favorited? Which patterns are also theoreticaly possible, and what kind of mechanisms of transition are possible among the different patterns?

• Keywords: filotaksija; dinamički modeli
• Keywords (english): phyllotaxis; dynamical models
• Language: croatian
• URN:NBN: urn:nbn:hr:217:347808
• Study programme: Title: Physics and Computer Science; specializations in: Education; Course: Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike i informatike (magistar/magistra fizike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-03-04 16:32:15