Possible to make a Collatz fractal in Fractint?
Just wondering. https://en.m.wikipedia.org/wiki/Collatz_conjecture --- David W. Jones gnome@hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com Sent from my Android device with F/LOSS K-9 Mail.
Possible to make a Collatz fractal in Fractint? Just wondering. https://en.m.wikipedia.org/wiki/Collatz_conjecture -David W. Jones It might be possible. It would also depend on which view of the Collatz Conjecture's properties you want to display.
It's easy (and fun) to write the code to calculate and display the sequence of "hailstone numbers" referred to in the Collatz conjecture in a normal development environment. However, if you want to use Fractint to show the sequence of hailstone numbers galloping along or the properties of the members of the sequence, like "stopping time" or "highest number reached," it could be a fussy proposition -- given Fractint's pixel writing sequencing assumptions... It may be possible to force existing Fractint built-in formula types to write a pixel to a given (X, Y) location... E.g.: I saw in the Fractint Docs that L-Systems have "Move Forward" and "Draw Forward" commands, although I don't immediately see a practical way to use this particular draw command because of the L-system framework it's included in. Anyone know if there's a way for a Fractint *formula* to write a pixel to a given (X, Y) location -- the way that Fractint's built-in orbit fractal formulas (like Lorenz) do? The 20.0 Fractint docs say that "scrnpix" is a "Predefined Variable (x, y)": scrnpix (col, row) pixel screen coordinates. (col, row) ranges from (0,0) to (xdots-1, ydots-1) but I don't know if it's read only or what Fractint's behavior is if you write to it. Anyone know? - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: David W. Jones <gnome@hawaii.rr.com> Sent: Tuesday, November 30, 2021 10:39 PM To: Fractint List <Fractint@mailman.xmission.com> Subject: [Fractint] Possible to make a Collatz fractal in Fractint? Importance: High Just wondering. https://en.m.wikipedia.org/wiki/Collatz_conjecture --- David W. Jones gnome@hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com Sent from my Android device with F/LOSS K-9 Mail. _______________________________________________ Fractint mailing list -- fractint@mailman.xmission.com To unsubscribe send an email to fractint-leave@mailman.xmission.com
On Wed, Dec 1, 2021 at 8:43 PM Harold Lane <hallane@earthlink.net> wrote:
Possible to make a Collatz fractal in Fractint? Just wondering. https://en.m.wikipedia.org/wiki/Collatz_conjecture -David W. Jones It might be possible. It would also depend on which view of the Collatz Conjecture's properties you want to display.
You can enter it as a regular escape fractal and that should work just fine. Since it is a one dimensional fractal it will be boring. The code below is my cut at it translated from Fracton into FractInt language. The image looks like a bunch of vertical stripes since as a one dimensional fractal it only changes in x. Fracton's histogram looked similar to the Wikipedia article except for a more pronounced dip that is barely noticeable in the Wikipedia pages. To get the histogram in FractInt, change the color map to a grayscale map and export the fractal image. Make a histogram of the image in Photoshop or some other image processing program. Collatz { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20211202_1223 passes=1 float=y center-mag=3.5/0/0.3809523857142857/1/0/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=300 inside=1 proximity=0 colors=000SNCTNCUODVPEWQFXRGYSHZTH`UIaVJbWKcXLdYMe\ ZMf_Ng`OiaPjbQkcRldRmeSnfTogUphVriWsjWtkXulYvmZwn_\ xo`zpaypaxo`wn_vm_ulZtkYsjXriXqhWpgVogUnfUmeTldSkc\ RibRhaQg`Pf_OeZOdZNcYMbXLaWL`VK_UJZTIYSIXRHWQGUPF0\ 00111333555666888AAABBBDDDFFFHHHIIIKKKMMMNNNPPPRRR\ TTTUUUWWWYYYZZZ```bbbdddeeegggiiijjjlllnnnpppooomm\ mllljjjhhhgggeeecccbbb```ZZZYYYWWWUUUTTTRRRPPPOOOM\ MMKKKJJJHHHFFFEEECCCAAA999777555444222000PFFQFFRGF\ SHFTIFVJFWKFXLFYMF_NF`OFaOEbPEcQEeREfSEgTEhUEjVEkW\ ElXEmXDnYDpZDq_Dr`DsaDubDvcDwdDxeDzfCyfCxeCwdCvcCu\ bCsaCr`Cq_Cp_CoZCmYDlXDkWDjVDiUDgTDfTDeSDdRDcQDbPD\ `OE_NEZMEYMEXLEVKEUJETIESHERGEPFF00K00L11M11N22O22\ P33Q33S44T44U55V66W66X77Z77_88`88a99b99cAAeAAfBBgC\ ChCCiDDjDDlEEmEEnFFoFFpGGqHHsHHrGGqGGpFFoFFnEEmEEl\ DDjDDiCChCCgBBfBBeAAdAAc99a88`88_77Z77Y66X66W55V55\ T44S44R33Q33P22O22N11M00K } frm:F_20211202_1223 { ; Enter a fractal formula here. z=floor(100*real(pixel)): if(z%2),z=3*z+1,else,z=z/2,endif, z>1 } -- Mike Frazier www.fracton.org
participants (3)
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David W. Jones -
Harold Lane -
Mike Frazier