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: The Mandelbrot Set Logistic Equation, Etc Julia Sets Newton Fractals § 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.

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  Continue or  Return to the Top:

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).

Continue or  Return to the Top: 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 Continue or  Return to the Top:

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 Continue or  Return to the Top:

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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Gallery 2D: The Mandelbrot Set Logistic Equation, Etc Julia Sets Newton Fractals Gallery 3D: Fractal Mountains and Forests Fantasy Landscapes Fractals on Nonplanar Surfaces 