Magic Cauldron

Transformation around the cauldron

101

นิพจน์ 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 0

112

CAULDRON

113

Universal cauldron functions

114

Bubbling parameter

120

Bubbling

134

Bubbling independently animated

145

Cauldron

150

Running dog pattern

157

Sun

168

Sun independently animated

179

Face of sun

182

Moon

191

Ocean

207

Ocean independently animated

214

Stand

217

Patterns of the cauldron with one implicit inequality:

227

นิพจน์ 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

นิพจน์ 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 0

230

นิพจน์ 231: "C" Subscript, "r" "e" "d" , Baseline equals rgb left parenthesis, 255 , 0 , 0 , right parenthesis

231

232

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