Sekino's Fractal Art Gallery 2D

The gallery comprises fractal images that can be plotted on a plane by standard programming routines described in Stories about Fractal Plotting. We classify the images into four groups:





§ 3. Julia Sets



Running Corollas


 This is a Julia set given by the Mandelbrot equation zn+1 = zn2 + p with p = (-1.1128, 0.23076). The period of the Julia set is 54, i.e., the interior of the gold Julia set comprises the initial values of orbits that converge to a 54-cycle. Can you see the number 54 = 2 x 3 x 9 in the shape of the Julia set?










Walking Corollas
Dancing Corollas

These are essentially the same Julia set, which is given by the dynamical system zn+1 = p(1 - zn5) zn with p = (-0.78, 0.645).












Julia Elephants

This is a Julia set of period 1 given by the Logistic equation zn+1 = p(1 - zn) zn with p = (3.001, 0.075975). A smaller period does not mean a simpler image.






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Julia Lion 42

This is the Julia set given by the Mandelbrot equation zn+1 = zn2 + p with p = (0.296555, 0.020525). The period of the Julia set is 42 = 3 x 14.










Julia Lion 68










Julia Lion 85
Julia Lion 85






· · ·   morphing into   · · ·





Hydrae of Lerna






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Hydra of Lerna with Eleven Heads

This is a Julia set of period 9 given by the Mandelbrot equation zn+1 = zn2 + p with p = (-0.692712, 0.273012).










Hydra of Lerna with Nine Heads










Hydra of Lerna with Six Heads

This is a Julia set of period 6 given by the dynamical system zn+1 = zn3 + zn + p with p = (0.1968, 0.0008).






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The Blue Rose of Baghdad










Blue Roses by the dynamical system zn+1 = p(1 + zn)(1 - zn) zn


With p = (0.81168, 0.58533)

With p = (0.971, 0.240)






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Julia Pansies

This is the Julia set given by the Mandelbrot equation zn+1 = zn2 + p with p = (0.250100022, 0.000001992).










Julia Butterflies






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Partying Seahorses






· · ·   morphing into   · · ·





Potbellied Seahorses






· · ·   morphing into   · · ·





Circus Elephants

Stare the elephants in action and you'll see them coming out of the frame. Stare and you'll see a 3D picture · · ·






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Dancing Seahorses




















Dancing Beans






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Twin Dragons

This is a Julia set given by the Dynamical System   zn+1 = zn3 + zn + p .





















Twin Dragons

This is a Julia set given by the Dynamical System  zn+1 = p(1 + zn)(1 - zn) zn .



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