= Period-two bulb of the Mandelbrot set
{title2=$|c+1|<1/4$}
= Period-two bulb
{synonym}
The period-two bulb is the open disc $|c+1|<1/4$ of quadratic parameters with an attracting exact two-cycle. The points in that cycle are roots of $z^2+z+c+1$, whose product is $c+1$. Its multiplier is therefore $4(c+1)$, giving precisely the disc inequality. At $c=-3/4$ the two roots merge into the fixed point $-1/2$, whose original multiplier is minus one; the second iterate has multiplier one and a triple fixed-point root. This boundary point is the attachment to the <main cardioid>.
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