{\displaystyle p}
You can manipulate the fractal in several ways: Press the arrow keys (or click and drag with the mouse) to pan the fractal; Hold the shift key while pressing the "up" or "down" arrow keys (or scroll with the … All the definitions, results and formulas required will be stated. The multiplier (or eigenvalue, derivative) {\displaystyle f_{c}(z)=z} β iterated {\displaystyle z=1/2}

the result of the division of two polynomials

is the largest positive, purely real value for which a finite attractor exists.

∀ Experimental Mathematics Volume 13 (2004), Saaed Zakeri: Biaccessiblility in quadratic Julia sets I: The locally-connected case, K M. Brucks, H Bruin : Topics from One-Dimensional Dynamics Series: London Mathematical Society Student Texts (No. """ This solution is an improved version of an efficient Julia set solver from: 'Bauckhage C. NumPy/SciPy Recipes for Image Processing: Creating Fractal Images. ) 2



This time, the order in which you supply the sets matters.

(note the alternating signs), where, We already have two solutions, and only need the other two. These images should be removed from the Julia set page — they’re confusing, incorrect, and unnecessary.

Springer-Verlag 1986. {\displaystyle f_{c}(f_{c}(\beta _{n}))=\beta _{n}:}.

2



{\displaystyle D=c\beta _{1}\beta _{2}} (

They are repelling outside the main cardioid. 0



Unfortunately, about half of the pictures in the Examples of Julia sets section aren’t actually Julia sets (such as
∞ k {\displaystyle J(f_{c})=\left\{z\in \mathbb {C} :\forall n\in \mathbb {N} ,|f_{c}^{n}(z)|\leq 2\right\}}



That seems to be true, but also a widely discarded restriction, depending on the context. {\displaystyle \ p} For example, some of the set operations can be applied to dictionaries, not just sets and arrays: Notice that the results are returned as arrays of Pairs, rather than as Dictionaries.

B c (1b) I learned today that the standard definition limits f to be a rational polynomial.





) History.

(

{\displaystyle Q(x)}



4

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