Calculation of the Structure of a Shrub in the Mandelbrot Set

<table>Mandelbrot set and a sketch of the antenna showing the first three chaotic bands <svg height="16.512501" id="M79" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 18.0625 16.512501" width="18.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, <svg height="16.375" id="M80" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 18.0625 16.375" width="18.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, and <svg height="16.375" id="M81" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 18.0625 16.375" width="18.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.675)"><path d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62
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</svg> separated by the merging points <svg height="13.0875" id="M82" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 18.525 13.0875" width="18.525" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,14.037,12.313)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
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</svg>. In each chaotic band, the reduced EAs of the first LLAHCs are shown.</table>

Discrete Dynamics in Nature and Society

Calculation of the Structure of a Shrub in the Mandelbrot Set

Figure 3