Expression 112: "f" Subscript, "f" "i" "r" "e" , Baseline left parenthesis, "f" Subscript, "b" "i" "n" "p" , Baseline left parenthesis, "x" , "y" , "x" Subscript, 1 , Baseline , "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis . "x" , "f" Subscript, "b" "i" "n" "p" , Baseline left parenthesis, "x" , "y" , "x" Subscript, 1 , Baseline , "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis . "y" , right parenthesis greater than or equal to 0ffirefbinpx,y,x1,y1,Ra.x,fbinpx,y,x1,y1,Ra.y≥0
112
CAULDRON
113
Universal cauldron functions
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114
Bubbling parameter
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120
Bubbling
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134
Bubbling independently animated
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145
Cauldron
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150
Running dog pattern
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157
Sun
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168
Sun independently animated
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179
Face of sun
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182
Moon
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191
Ocean
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207
Ocean independently animated
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214
Stand
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217
Patterns of the cauldron with one implicit inequality:
227
Expression 228: 4 minus "B" left parenthesis, "M" Subscript, "o" "o" "n" , Baseline left parenthesis, StartFraction, phi Subscript, "x" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "x" 2 , Baseline Over "R" Subscript, "s" "u" "n" , Baseline "s" Subscript, "c" "a" "l" "e" , Baseline "s" Subscript, "c" "a" "l" "e" "m" , Baseline , EndFraction , StartFraction, phi Subscript, "y" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "y" 2 , Baseline Over "R" Subscript, "s" "u" "n" , Baseline "s" Subscript, "c" "a" "l" "e" , Baseline "s" Subscript, "c" "a" "l" "e" "m" , Baseline , EndFraction , right parenthesis , right parenthesis minus "B" left parenthesis, "W" Subscript, "a" "v" "e" , Baseline left parenthesis, "l" Subscript, 2 , Baseline left parenthesis, phi Subscript, "x" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus StartFraction, "T" Over 3 , EndFraction , right parenthesis , "l" Subscript, 2 , Baseline phi Subscript, "y" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline "h" Subscript, "s" , Baseline , right parenthesis , right parenthesis minus "B" left parenthesis, "F" Subscript, "s" "u" "n" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "T" , right parenthesis , right parenthesis minus "B" left parenthesis, left parenthesis, StartFraction, phi Subscript, "x" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "x" , Baseline Over 5 thirds "s" Subscript, "c" "a" "l" "e" , Baseline , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, phi Subscript, "y" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "y" , Baseline Over 5 thirds "s" Subscript, "c" "a" "l" "e" , Baseline , EndFraction , right parenthesis squared minus 0.8 5 squared , right parenthesis minus "B" left parenthesis, "F" Subscript, "a" "c" "e" , Baseline left parenthesis, "s" Subscript, "f" "c" , Baseline left parenthesis, StartFraction, phi Subscript, "x" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "x" , Baseline Over 5 thirds "s" Subscript, "c" "a" "l" "e" , Baseline , EndFraction , right parenthesis , "s" Subscript, "f" "c" , Baseline left parenthesis, left parenthesis, StartFraction, phi Subscript, "y" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus theta Subscript, "y" , Baseline Over 5 thirds "s" Subscript, "c" "a" "l" "e" , Baseline , EndFraction , right parenthesis , right parenthesis plus 0.2 , right parenthesis , right parenthesis plus "B" left parenthesis, "R" Subscript, "D" , Baseline left parenthesis, "l" phi Subscript, "x" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis , "l" left parenthesis, phi Subscript, "y" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis minus "h" Subscript, "k" , Baseline , right parenthesis , right parenthesis , right parenthesis greater than or equal to 04−BMoonϕxx−x1,y−y1,Ra−θx2Rsunscalescalem,ϕyx−x1,y−y1,Ra−θy2Rsunscalescalem−BWavel2ϕxx−x1,y−y1,Ra−T3,l2ϕyx−x1,y−y1,Ra+l2hs−BFsunx−x1,y−y1,T−Bϕxx−x1,y−y1,Ra−θx53scale2+ϕyx−x1,y−y1,Ra−θy53scale2−0.852−BFacesfcϕxx−x1,y−y1,Ra−θx53scale,sfcϕyx−x1,y−y1,Ra−θy53scale+0.2+BRDlϕxx−x1,y−y1,Ra,lϕyx−x1,y−y1,Ra−hk≥0
228
Things outside the cauldron with one inequality:
229
Expression 230: left parenthesis, "B" left parenthesis, left parenthesis, "B" left parenthesis, "F" Subscript, "o" "a" "m" , Baseline left parenthesis, "s" Subscript, "c" , Baseline StartFraction, "x" minus "x" Subscript, 1 , Baseline Over "R" Subscript, "a" , Baseline , EndFraction , "s" Subscript, "c" , Baseline left parenthesis, StartFraction, "y" minus "y" Subscript, 1 , Baseline Over "R" Subscript, "a" , Baseline , EndFraction minus "p" Subscript, "y" , Baseline , right parenthesis , "A" Subscript, "f" , Baseline , right parenthesis , right parenthesis minus "B" left parenthesis, "F" Subscript, "c" "a" "u" "l" "d" "r" "o" "n" , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , "y" minus "y" Subscript, 1 , Baseline , right parenthesis , right parenthesis plus 1 minus "B" left parenthesis, "f" Subscript, "f" "i" "r" "e" , Baseline left parenthesis, "f" Subscript, "b" "i" "n" "p" , Baseline left parenthesis, "x" , "y" , "x" Subscript, 1 , Baseline , "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis . "x" , "f" Subscript, "b" "i" "n" "p" , Baseline left parenthesis, "x" , "y" , "x" Subscript, 1 , Baseline , "y" Subscript, 1 , Baseline , "R" Subscript, "a" , Baseline , right parenthesis . "y" , right parenthesis , right parenthesis , right parenthesis , right parenthesis minus "B" left parenthesis, Start sum from "i" equals 1 to StartFraction, length left parenthesis, "x" Subscript, 6 , Baseline , right parenthesis Over 2 , EndFraction , end sum, "B" left parenthesis, "f" Subscript, "e" "g" "g" , Baseline left parenthesis, "x" , "y" , "x" Subscript, 6 , Baseline left bracket, 2 "i" minus 1 , right bracket , "x" Subscript, 6 , Baseline left bracket, 2 "i" , right bracket , "y" Subscript, 6 , Baseline left bracket, 2 "i" minus 1 , right bracket , "y" Subscript, 6 , Baseline left bracket, 2 "i" , right bracket , 4 , "r" Subscript, "b" "o" "n" , Baseline left bracket, "i" , right bracket , right parenthesis , right parenthesis , right parenthesis , right parenthesis squared greater than or equal to 0BBFoamscx−x1Ra,scy−y1Ra−py,Af−BFcauldronx−x1,y−y1+1−Bffirefbinpx,y,x1,y1,Ra.x,fbinpx,y,x1,y1,Ra.y−Blengthx62∑i=1Bfeggx,y,x62i−1,x62i,y62i−1,y62i,4,rboni2≥0
