Expression 4: Start product from "i" equals negative "y" to sign left parenthesis, StartRoot, "x" plus "y" minus StartAbsoluteValue, "x" minus "y" , EndAbsoluteValue , EndRoot , right parenthesis , end product, left parenthesis, 1 plus sign left parenthesis, .5 plus max left parenthesis, cos left parenthesis, 3 Superscript, "i" , Baseline "x" , right parenthesis , cos left parenthesis, 3 Superscript, "i" , Baseline "y" , right parenthesis , right parenthesis , right parenthesis , right parenthesis greater than or equal to 0signx+y−x−y∏i=−y1+sign.5+maxcos3ix,cos3iy≥0
4
Sierpiński Hexagon:
5
Expression 6: Start product from "i" equals negative left parenthesis, "x" plus StartRoot, 3 , EndRoot "y" , right parenthesis to sign left parenthesis, StartRoot, StartRoot, 3 , EndRoot left parenthesis, "x" minus StartAbsoluteValue, "x" , EndAbsoluteValue , right parenthesis plus 2 "y" , EndRoot , right parenthesis , end product, left parenthesis, 1 plus sign left parenthesis, 1 plus StartAbsoluteValue, mod left parenthesis, 3 Superscript, "i" , Baseline "y" minus 1 , 2 , right parenthesis minus 1 , EndAbsoluteValue minus StartAbsoluteValue, mod left parenthesis, 3 Superscript, "i" plus .5 , Baseline "x" minus sign left parenthesis, sin left parenthesis, StartFraction, pi Over 2 , EndFraction 3 Superscript, "i" , Baseline "y" , right parenthesis cos left parenthesis, StartFraction, pi Over 2 , EndFraction 3 Superscript, "i" minus .5 , Baseline "x" , right parenthesis , right parenthesis minus 3 , 6 , right parenthesis minus 3 , EndAbsoluteValue , right parenthesis , right parenthesis greater than or equal to 0sign3x−x+2y∏i=−x+3y1+sign1+mod3iy−1,2−1−mod3i+.5x−signsinπ23iycosπ23i−.5x−3,6−3≥0
6
Hexaflake:
7
Expression 8: Start product from "i" equals negative left parenthesis, "x" plus StartRoot, 3 , EndRoot "y" , right parenthesis to sign left parenthesis, StartRoot, StartRoot, 3 , EndRoot left parenthesis, "x" minus StartAbsoluteValue, "x" , EndAbsoluteValue , right parenthesis plus 2 "y" , EndRoot , right parenthesis , end product, left parenthesis, 1 plus sign left parenthesis, sin squared left parenthesis, StartFraction, pi Over 2 , EndFraction 3 Superscript, "i" , Baseline "y" , right parenthesis plus sin left parenthesis, StartFraction, pi Over 2 , EndFraction 3 Superscript, "i" , Baseline "y" , right parenthesis sin left parenthesis, StartFraction, pi Over 2 , EndFraction 3 Superscript, "i" plus .5 , Baseline "x" , right parenthesis , right parenthesis , right parenthesis greater than or equal to 0sign3x−x+2y∏i=−x+3y1+signsin2π23iy+sinπ23iysinπ23i+.5x≥0