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A194473 Decimal expansion of the area of the fourth Mandelbrot set lemniscate 1
3, 2, 7, 9, 1, 8, 5, 8, 3, 3, 3, 8, 6, 6, 8, 2, 4, 8, 1, 7, 0, 1, 1, 3, 0, 2, 0, 6, 2, 5, 2, 3, 1, 4, 6, 2, 0, 3, 7, 0, 1, 4, 3, 4, 9, 0, 0, 9, 5, 7, 5, 0, 9, 8, 0, 4, 5, 8, 6, 1, 3, 7, 5, 3, 4, 2, 0, 2, 3, 6, 3, 2, 0, 2, 2, 6, 1, 5, 0, 9, 5, 0, 4, 0, 7, 6, 5, 5, 4, 6, 0, 3, 3, 9, 9, 2, 1, 1, 9, 9, 6, 3, 3, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Mandelbrot Set Lemniscate

EXAMPLE

3.279185833...

MATHEMATICA

f[x_, y_] = ComplexExpand[#*Conjugate[#] &[c + (c + (c + c^2)^2)^2] /. c -> x + I*y] - 4 ; sy = Solve[f[x, y] == 0, y]; sx = Solve[f[x, y] == 0, x]; f1[x_] = y /. sy[[8]]; f2[x_] = y /. sy[[4]]; g1[y_] = x /. sx[[1]]; g2[y_] = x /. sx[[2]]; x1 = -39/20; y1 = f1[x1]; x2 = -7/4; y2 = f1[x2]; x3 = -1; y3 = f2[x3]; x4 = -1/10; y4 = f2[x4]; x5 = 107/200; y5 = f1[x5]; x6 = 10703/20000; y6 = f1[x6];

  ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120];

i1 = ni[-g1[y] + g1[y1], {y, 0, y1}];

i2 = ni[f1[x], {x, x1, x2}];

i3 = ni[-g1[y] + g1[y3], {y, y2, y3}] + (x3 - x2) y2;

i4 = ni[f2[x], {x, x3, x4}] ;

i5 = ni[g2[y] - g2[y4], {y, y5, y4}] + (x5 - x4) y5 ;

i6 = ni[f1[x], {x, x5, x6}] ;

i7 = ni[ g2[y] - g2[y6], {y, 0, y6}];

area = 2 (i1 + i2 + i3 + i4 + i5 + i6 + i7);

Take[RealDigits[area][[1]], 105]

CROSSREFS

Cf. A194474 (perimeter)

Sequence in context: A245581 A054170 A106167 * A091913 A212285 A192789

Adjacent sequences:  A194470 A194471 A194472 * A194474 A194475 A194476

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Aug 26 2011

STATUS

approved

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Last modified May 12 02:06 EDT 2021. Contains 343808 sequences. (Running on oeis4.)