GSP4„¬›è†QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.8$èÐþÑèLSierpinski Right Triangle` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0526/Feb 28 20030#H±Arial
±Geneva§³³ '''$'ÿ$'€$'€$'ÿÿ$'€€$'€$'ÿÿ$'ÿÿÿ$'ÀÀÀ$' $'
$'%'&'8'8'8'9':'ÐÿÕ˜nÁQ\aAAØ™\@àl@×ÐÿÕ˜nÁQ\aABØ™@{@ m@×ÐÿÒ$Óð¿Ðrï¼€V@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@4Ò
¤34×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×é‡è†QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.8$è-×(LSierpinski 3 Point Triangle` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0526/Feb 28 20030#H±Arial
±Geneva©³³ '''$'ÿ$'€$'€$'ÿÿ$'€€$'€$'ÿÿ$'ÿÿÿ$'ÀÀÀ$' $'
$'%'&'8'8'8'9':'ÐÿÕ˜nÁQ\aAAØ™`i@0{@×ÐÿÕ˜nÁQ\aACØ™@x@@i@×ÐÿÕ˜nÁQ\aABØ™ ˆ@°v@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@@Ò
Ûxb>×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×ÐÿÕ˜nÁQ\aACØ™€y@Àk@×ÐÿÕ˜nÁQ\aABØ™àk@p|@×ÐÿÕ˜nÁQ\aAAØ™Àˆ@ðw@×ÐÿÒ
Óà?×ÐÿÒÓà?×ÐÿÒ
Óà?×ÐL@@Ò
Ûxb>×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×ÐÿÕ˜nÁQ\aACØ™Àz@@n@×ÐÿÕ˜nÁQ\aABØ™`n@°}@×ÐÿÕ˜nÁQ\aAAØ™`‰@0y@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@@Ò
Ûxb>×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×ÐÿÕ˜nÁQ\aAAØ™Š@pz@×ÐÿÕ˜nÁQ\aABØ™pp@ð~@×ÐÿÕ˜nÁQ\aACØ™|@`p@×ÐÿÒ Óà?×ÐÿÒ! Óà?×ÐÿÒ!Óà?×ÐL@@Ò ! #"#!$"$"#$
Ûxb>×ÐMAÿÒ"%×ÐMAÿÒ#%×ÐMAÿÒ$%×$(# !"#$&'(é‡è†QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.8$ènÞ LSierpinski Equilateral Triangle` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0526/Feb 28 20030#H±Arial
±Geneva©³³ '''$'ÿ$'€$'€$'ÿÿ$'€€$'€$'ÿÿ$'ÿÿÿ$'ÀÀÀ$' $'
$'%'&'8'8'8'9':'ÐÿÕ˜nÁQ\aAAØ™ðp@pw@×ÐÿÕ˜nÁQ\aABØ™0‚@0w@×ÐÿÒ$ÓµLXèz¶ë¿Üÿÿÿÿÿß?N@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@4Ò
Ç5¼9×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×ÐMAÿÒ×((#
é‡ö†d{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êLRight Sierpinski Fractal±Arial
±Geneva§³³ ÐÕ˜nÁQ\aABØ™
×ÐÕ˜nÁQ\aAAØ™×ÐÿÒ$Óð¿Ðrï¼€V@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@4Ò
¤34Õ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[2]×ÐMAÿÒÕ˜nÁQ\aA[3]×ÐMAÿÒÕ˜nÁQ\aA[4]×´p/#This Sierpinski Fractal tool constructs a resizable Sierpinski right triangle that displays the set of "new" midpoints that are constructed by the three iteration maps. The set of all such constructed points (an infinite set of points) is the true Sierpinski Right Triangle Fractal.
Created by Virginia R. Jones on December 24, 2003.
e-mail address: jonesv@ccsu.eduë‡ö†d{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ê
LSierpinski 3 Point Fractal±Arial
±Geneva©³³ ÐÕ˜nÁQ\aACØ™ FiØü‚²×ÐÕ˜nÁQ\aAAØ™x‡@p~@×ÐÕ˜nÁQ\aABØ™t†@Ú|@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@@Ò
Ûxb>Õ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[2]×ÐMAÿÒÕ˜nÁQ\aA[3]×´¢/#This tool creates the Sierpinski Triangle Fractal from any set of three non-collinear points. By creating the midpoints of the segments of the triangle whose vertices are the three "given" points, and repeating this midpoint construction process on each new triangle formed, the points of the Sierpinski Triangle Fractal are created.
Created by Virginia R. Jones on December 24, 2003.
e-mail address: jonesv@ccsu.eduë‡ö†d{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ê LSierpinski Equilateral Triangle±Arial
±Geneva§³³ ÐÕ˜nÁQ\aABØ™)cA×ÐÕ˜nÁQ\aAAØ™2RA×ÐÿÒ$ÓµLXèz¶ë¿Üÿÿÿÿÿß?N@×ÐÿÒÓà?×ÐÿÒÓà?×ÐÿÒÓà?×ÐL@4Ò
Ç5¼9Õ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[1]×ÐMAÿÒÕ˜nÁQ\aA[2]×ÐMAÿÒÕ˜nÁQ\aA[3]×ÐMAÿÒÕ˜nÁQ\aA[4]×´”/#This tool creates the "classic" Sierpinski Triangle Fractal - an equilateral triangle. It is based on two points. After one point is rotated about the other point by 60 degrees, the three vertices of a equilateral triangle have been created. The iteration maps for this fractal require only the original two points.
Created by Virginia R. Jones on December 24, 2003.
e-mail address: jonesv@ccsu.eduë‡…