#wxpython

The mandel a number based on z - z**n + c using the Number Abstract Base Class in Python.

Here is an Idea that I have had for a while but until the ABC I couldn't get a framework together.

The code; https://pastebin.com/04dFRaDa

The mandel works like this,

All internal calculations are done in Fd so import both numbers from newnumber.

    from newnumber import Fd,mandel

Some definitions are in order. The infinite string of numbers created by  z**n + c  is called a soul line. If Z starts at (0,0,0) the sole line is said to be root. If Z starts off of the root soul line it is called an aura. The soul pointer shows what iteration the number lies on and is meaningless for auras.

The inputs are (C, Z, dimension, soul pointer),

    c = mandel(1,0,0,0)

    for i in range(10):         print(c.Z())        c.increment_sp()

    (0.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (2.0+0.0j+0.0k)

Zero dimensional mandel’s are constants and all aura’s are root.

Operations mandel to mandel are Z to Z , C to C . I wasn't sure how to handle dimensions so +- is lower of the two and */ is higher of the two. Operation result in an aura and the soulp is set to the highest of the two.

    a = mandel(1,1,0,0)

    b = a + c

    print(b)     C : (2.0+0.0j+0.0k)     Z : (3.0+0.0j+0.0k)     Dim : 0     Soulp : 10     Aura : True

Operations mandel to x are C to x, Z to x.

    b = a*5

    print(b)     C : (5.0+0.0j+0.0k)     Z : (5.0+0.0j+0.0k)     Dim : 0     Soulp : 0     Aura : True

One dimensional mandel’s are linear.

    a = mandel(1,0,1,0)

    for i in range(10):

        print(a.Z())         a.increment_sp()

    (0.0+0.0j+0.0k)     (1.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (3.0+0.0j+0.0k)     (4.0+0.0j+0.0k)     (5.0+0.0j+0.0k)     (6.0+0.0j+0.0k)     (7.0+0.0j+0.0k)     (8.0+0.0j+0.0k)     (9.0+0.0j+0.0k)

Two dimensional and beyond are exponential.

    a = mandel(1,0,2,0)

    for i in range(10):         print(a.Z())         a.increment_sp()

    (0.0+0.0j+0.0k)     (1.0+0.0j+0.0k)     (2.0+0.0j+0.0k)     (5.0+0.0j+0.0k)     (26.0+0.0j+0.0k)     (677.0+0.0j+0.0k)     (458330.0+0.0j+0.0k)     (210066391040.0+0.0j+0.0k)     (4.412788594124235e+22+0.0j+0.0k)     (inf+0.0j+0.0k)

Here is one number from the Twins.

    a = mandel(Fd(-.7, 0.1333333333333333,.2),Fd(0,0,0),5,0)

    for i in range(10):         print(a.Z())        a.increment_sp()

    (0.0+0.0j+0.0k)     (-0.699999988079071+0.13333334028720856j+0.20000000298023224k)     (-0.6512947082519531+0.2626233696937561j+0.39393505454063416k)     (-0.3355112373828888+0.16607318818569183j+0.24910977482795715k)     (-0.684900164604187+0.13019981980323792j+0.19529972970485687k)     (-0.65702885389328+0.24914729595184326j+0.3737209439277649k)     (-0.3504582643508911+0.1886182278394699j+0.28292733430862427k)     (-0.6823979616165161+0.12573394179344177j+0.18860089778900146k)     (-0.6684328317642212+0.24513068795204163j+0.36769604682922363k)     (-0.33876651525497437+0.2036655992269516j+0.3054983913898468k)

Power has not been implemented yet.

Here is GLcanvas example of the Twins using the mandel.

https://pastebin.com/5MaR4GP6

GLcanvis test for WXPython Phoenix using Fd fractals.

Here’s the code.

https://pastebin.com/3mCiSWJv

needs the Fd script,

https://pastebin.com/DvPWGuF0

Here is 435 interesting Fd’s

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