Mandelbrot Sequences and Orbits
...which correspond to them. Almost all the entries are focused on points near a bulb of period 14, attached to the main cardiod. Send entry suggestions to: Entry Editor

Each entry of this encyclopedia is a complex number c = x+ yi. The sequence associated to this number is found by iterating z_(n+1) = (z_n)^2 + c.

Pictured are the plotted terms in the sequence, graphed using javascript.
Cut and paste the value into interactive animated javascript, with suggested zoom, to see the sequence animated.

Below each picture is a designation of whether the original number is in the Mandelbrot set M or not; that is, whether its sequence is bounded or not.

The link in each entry to the wolfram alpha plot will give an approximate location, and an approximate Julia set.
SEQUENCES
Density
 (Is in M) c = -0.260143 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 900.Some that got away:-0.26077 + 0.6337i -0.26071 + 0.6337i -0.2608 + 0.6337i
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White hole sun
 (Is not in M) c = -0.26036 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 1000. interactive animated javascript with pause and hold: use zoom = 1000.
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Fractal Periodic (period of 7*95)
 (Is in M) c = -0.260355 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 1000. 95 tiny spirals: -0.2603471 + 0.6337i
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Star: 14 bent spiral arms
 (Is in M) c = -0.257 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 900.
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Counter Star: counterclockwise
 (Is in M) c = -0.255 + 0.63345i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Sunflower
 (Is in M) c = -0.24 + 0.635i wolfram alpha plot. interactive animated javascript: use zoom = 1200.
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Space
 (Is in M) c = -0.26 + 0.6332i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Counter Space
 (Is in M) c = -0.25 + 0.6355558i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Crossed Scallop
 (Is in M) c = -0.26 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 900. 2-tone version: see 204 arms Even more arms: -0.26012 + 0.6337i
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Whirled
 (Is in M) c = -0.257 + 0.63432i wolfram alpha plot. interactive animated javascript: use zoom = 1200.
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Counter Whirled
 (Is in M) c -0.2548 + 0.6345i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Whirlier
 (Is not in M) c = -0.257 + 0.634456i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Whirliest
 (Is not in M) c = -0.25733999 + 0.634456i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Center cannot hold
 (Is not in M) c = -0.2573399923 + 0.63445602i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Period of 81 points
 (Is in M) c = -0.261 + 0.6337i wolfram alpha plot. interactive animated javascript: use zoom = 1000. 95 tiny spirals: -0.2603471 + 0.6337i Period 3x81 ? -0.261189 + 0.6337i Totoro ? -0.2612 + 0.6337i Screensaver: -0.2612 + 0.63373i
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Lesser Chaos
 (Is in M) c = -0.256625459 + 0.6345309i wolfram alpha plot. interactive animated javascript: use zoom = 875. Worth a try: -0.256625459 + 0.6345312i (gappy chaos) -0.256625459 + 0.634501i (super whirly)
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Not Whirly
 (Is not in M) c = -0.257341 + 0.634456i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Party Time
 (Is not in M) c = -0.256625459 + 0.634532i wolfram alpha plot. interactive animated javascript: use zoom = 860.
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Frayed Knot
 (Is not in M) c = -0.2566254588 + 0.634532i wolfram alpha plot. interactive animated javascript: use zoom = 860.
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Semi Chaos
 (Is not in M) c = -0.2625107 + .64i wolfram alpha plot. interactive animated javascript: use zoom = 1000.
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Repelled from center four times
 (Is not in M) c = -0.2599966743201 + 0.6350001i wolfram alpha plot. interactive animated javascript: use zoom = 900.
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14 plus one repelling points
 (Is not in M) c = -0.2601112 + 0.63537781i wolfram alpha plot. interactive animated javascript: use zoom = 900.
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14 mini 22-arm spirals
 (Is in M) c = -0.26 + 0.635375i wolfram alpha plot. interactive animated javascript: use zoom = 900.
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3 armed Spiral
 (Is in M) c = -0.14832 + 0.646999i wolfram alpha plot. interactive animated javascript: use zoom = 1200.
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Three 1-armed spirals
 (Is in M) c = -0.145 + 0.654i wolfram alpha plot. interactive animated javascript: use zoom = 1200.
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Chaos
 (Is in M) c = -0.01183223669 + 0.63816572702i wolfram alpha plot. interactive animated javascript: use zoom = 860.
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Misiurewicz point
 (Is in M) c = -0.77568377 + 0.13646737i wolfram alpha plot. wiki interactive animated javascript: use zoom = 920.
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[ slides]    [ Plot Mandlebrot sequences in Excel ]
...or even better in javascript.

Here's an excellent tutorial on the relationship between Mandelbrot and Julia sets, and on how the Fibonacci numbers appear.
Lots more in Mu-Ency... an encyclopedia of features of the Mandelbrot set.
Here's the Wolfram Mathworld article stating that it is unknown whether the Mandlebrot set is path connected.

A drag-and-drop demonstration of the orbits on a mandelbrot set.
...and a very nice mouse-over julia set generator.

Beautiful collection of lots more orbits by Stefan Bion; including composite pictures of orbits.
INDEX
##### DensityStar: 14 bent spiral armsWhite hole sunCounter Star: counterclockwiseFractal Periodic SunflowerSpaceCounter SpaceCrossed ScallopWhirledCounter WhirledWhirlierWhirliestCenter cannot holdPeriod of 81 pointsLesser ChaosNot WhirlyParty TimeFrayed KnotSemi ChaosRepelled from center four times 14 plus one repelling points14 mini 22-arm spirals3 armed SpiralThree 1-armed spiralsChaosMisiurewicz point

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