Experimentally (zooming in with a graphical Julia set computing program that I wrote) ages ago, the right edge of the central “circle” is at $\sim 0.109650026$ to within $10^{-9}$, whereas the top edge is at $\sim 0.107586829\cdot i$, so it's not a circle. And it's not an ellipse either, because the root point of the “$1/8$ antenna” is at $\sim 0.075332045 + 0.076747120\cdot i$, not on the obvious ellipse through the two previously mentioned points.
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