Expression 17: "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals "f" Subscript, 0 , Baseline left parenthesis, mod left parenthesis, 2 left parenthesis, "x" plus 1 , right parenthesis , 2 , right parenthesis minus 1 , right parenthesisf1x=f0mod2x+1,2−1
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Expression 18: "f" Subscript, "a" "d" "e" "I" "n" , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis minus "f" Subscript, 1 , Baseline left parenthesis, 0 , right parenthesis , right parenthesis left parenthesis, StartFraction, 1 Over 1 minus 2 "f" Subscript, 1 , Baseline left parenthesis, 0 , right parenthesis , EndFraction , right parenthesisfadeInx=f1x−f1011−2f10
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f0 = smooth transition between 0 to 1
f1 = repeat of f0 and faster
However, f0 & f1 never touches 0 and 1. They only approach it.
f_adeIn makes sure f(0) touches 0 and f(1) touches 1.
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Expression 20: "g" Subscript, "f" "a" "d" "e" "O" "u" "t" , Baseline left parenthesis, "t" , right parenthesis equals "g" left parenthesis, "t" , right parenthesis left bracket, "T" , right bracket times left parenthesis, 1 minus "f" Subscript, "a" "d" "e" "I" "n" , Baseline left parenthesis, "T" , right parenthesis , right parenthesisgfadeOutt=gtT·1−fadeInT
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Expression 21: "g" Subscript, "f" "a" "d" "e" "I" "n" , Baseline left parenthesis, "t" , right parenthesis equals "g" left parenthesis, "t" , right parenthesis left bracket, "T" plus 1 , right bracket times "f" Subscript, "a" "d" "e" "I" "n" , Baseline left parenthesis, "T" , right parenthesisgfadeInt=gtT+1·fadeInT
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Current graph fades out, while next graph fades in.
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Expression 23: "g" Subscript, "f" "a" "d" "e" "O" "u" "t" , Baseline left parenthesis, "t" , right parenthesis plus "g" Subscript, "f" "a" "d" "e" "I" "n" , Baseline left parenthesis, "t" , right parenthesisgfadeOutt+gfadeInt
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤