References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt160",{id:"formSmash:upper:j_idt160",widgetVar:"widget_formSmash_upper_j_idt160",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt161_j_idt163",{id:"formSmash:upper:j_idt161:j_idt163",widgetVar:"widget_formSmash_upper_j_idt161_j_idt163",target:"formSmash:upper:j_idt161:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Fractal Geometry, Graph and Tree ConstructionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2008 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2008. , 101 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-51347OAI: oai:DiVA.org:umu-51347DiVA: diva2:479178
##### Uppsok

Physics, Chemistry, Mathematics

#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt404",{id:"formSmash:j_idt404",widgetVar:"widget_formSmash_j_idt404",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt410",{id:"formSmash:j_idt410",widgetVar:"widget_formSmash_j_idt410",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt416",{id:"formSmash:j_idt416",widgetVar:"widget_formSmash_j_idt416",multiple:true});
Available from: 2012-03-01 Created: 2012-01-17 Last updated: 2012-03-01Bibliographically approved

In the 18th and 19th centuries the branch of mathematics that would later be known as fractal geometry was developed. It was the ideas of Benoˆıt Mandelbrot that made the area expand so rapidly as it has done recently, and since the publication of his works there have for fractals, and most commonly the estimation of the fractal dimension, been found uses in the most diverse applications. Fractal geometry has been used in information theory, economics, flow dynamics and image analysis, among many different areas.

This thesis covers the foundations of fractal geometry, and gives most of the fun- damental definitions and theorems that are needed to understand the area. Concepts such as measure and dimension are explained thoroughly, especially for the Hausdorff di- mension and the Box-counting dimension. An account of the graph-theoretic approach, which is a more general way to describe self-similar sets is given, as well as a tree- construction method that is shown to be equivalent to the graph-theoretic approach.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1120",{id:"formSmash:lower:j_idt1120",widgetVar:"widget_formSmash_lower_j_idt1120",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1121_j_idt1123",{id:"formSmash:lower:j_idt1121:j_idt1123",widgetVar:"widget_formSmash_lower_j_idt1121_j_idt1123",target:"formSmash:lower:j_idt1121:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});