CK12 - Geometry

• Extendthe patternin a self-similarfigure.

Introduction

In this lessonyou’lllearnaboutpatternscalledfractalsthat haveself-similarity. Insteadof usinga formal
definition,we’ll workwith a few examplesthat give the idea of self-similarity. In eachexampleyou will be
able to see that later stagesin a patternhavea similarityrelationshipto the originalfigure.

Example 1

The CantorSet

The patternin the diagrambelowis calledtheCantorSet, namedfor a creativemathematicianof the late
1800s.

The patterncontinues.Now let’s see why this patternis called“self-similar.”

Lookat the circledpart of the pattern.

You can see that eachpart of Level2 is similarto Level1 with a scalefactorof. The samerelationship
continuesas eachlevel is createdfrom the level beforeit.

Example 2

SierpinskiTriangle

To constructa SierpinskiTriangle,beginwith an equilateraltriangle.(Actually, any trianglecouldbe used.)
This is the Startlevel.