December 2021 - Fractint - mailman.xmission.com

Fracton 3D
by Mike Frazier 16 Dec '21

16 Dec '21

There is a new version of Fracton that supports 3D fractals. It also still supports FractInt parameter files. A new triplex compiler makes entering equations for 3D fractals as simple and concise as it was for 2D. Fracton then makes a 3D model with triangles. You compose the scene by moving the camera and adjusting lighting in real time. Once you are satisfied with the scene, Fracton can make a high quality ray traced image or a movie. Fracton is free and is available on the Mac App Store. https://apps.apple.com/app/id1589677006 -- Mike Frazier www.fracton.org

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3 and 4 dimensional Julia/Mandebrot sets using quaternions
by David W. Jones 16 Dec '21

16 Dec '21

From: Quaternion - Wikipedia https://en.m.wikipedia.org/wiki/Quaternion#Functions_of_a_quaternion_variab… Image: https://en.m.wikipedia.org/wiki/File:Quaternion_Julia_x%3D-0,75_y%3D-0,14.j… Image is a cross-section of a 4-dimensional fractal. --- David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com Sent from my Android device with F/LOSS K-9 Mail.

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Complex Collatz Fractal
by Mike Frazier 15 Dec '21

15 Dec '21

Here is another version of the Collatz fractal using complex numbers. I found some images on this link and a simpler formula than the one on Wikipedia (both give the same image though): https://yozh.org/2012/01/12/the_collatz_fractal/ Here is the PAR: Collatz2 { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20211202_1537 passes=1 float=y center-mag=0/0/0.3809523857142857/1/0/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=1000 inside=1 proximity=0 colors=000FLQQvgz`6`KP1vWH1zpVDeg86Zw`_w4hpK7pGHze\ pdkSSP8ZQj5HMDPjRg`CG6RtBZ8Re_jOCrWSUAGRKbetEe`DdF\ NJPhm_f9XSn`ehRV5g1WdcfHO8ryINGfDR1hE3KpG`ZfoqpnKT\ gXD_0ys7ZP7EnbS2ssyO`uCz4UuAhCWvvB0NGZiXnWL3rhl`_p\ PGVG5Jn0HGN6IIuCEqxRMQSCrHziJSMy08YJZ_P_tu94idZBBY\ 9`5LYhHYmTYxL`T7k79IqpR9PhG3aZNgK`AHRbjerpMRLhZ4gH\ GTNl57UigYV_NE_affhn7joo05yIDWQxEVQfnGkqH5WJxmSLeS\ GVqzJUC9c3VfVyEGlC89cyabbd2h27zwDE5sywwkQ_dX2cN5TH\ EaYzfzaLb2wnTxxtZ5VRh1HFzfcrbkiEwdrvs30wtYJqjkBgeR\ YFMzpH2XRBqWAdkU5q1a8pAciLP2n9U0ni3gZjR63cp2YXjXcu\ FN2GtWNpuz08b51LU6dWv9esETy5fPzO81_Ef0sZaDIoT7vba6\ 3JT8uBZPmwvucYcFKbGfUHhlLkvlFAp`Xd5E2KHsb3Z76m5ad9\ WonMODBkdxjdyNYtzIfgfQKdDErbFehLRN7gcV30pjDqCFOGXs\ 7J1x2KCeVZCvNXDz8oN3VzOQQa3v4jAJ2dPuB0U4XFVrJv954o\ PlI_oSCoY7ODXVhrm8RvcIYP2rwYdhgNQyWtKXMVzRuLNAtf5w\ heuN6l6JUDLdJeyUSRdZjg9Uy } frm:F_20211202_1537 { ; Collatz fractal z=pixel: ; Wikipedia formula commented out but gives same result ;cz = cos(z * pi / 2); ;sz = sin(z * pi / 2); ;z = (z / 2) * cz * cz + sz * sz * (3 * z + 1); z=(2+7*z-(2+5*z)*cos(pi*z))/4, |z|<100 } -- Mike Frazier www.fracton.org

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YouTube video: "How Imaginary Numbers Were Invented":
by Harold Lane 14 Dec '21

14 Dec '21

I just "chanced across" this YouTube video (it was "suggested" to me) -- meaning YouTube owner, Google, "knows" of my interest in fractals and imaginary numbers: "How Imaginary Numbers Were Invented": I enjoyed the clear steps shown in the video -- traveling thru historical mathematics -- that led to these special numbers that we enjoy the visual results of so much. I have a storage shed where I keep my imaginary numbers, but I don't ever let anyone see them... https://www.youtube.com/watch?v=cUzklzVXJwo - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Possible to make a Collatz fractal in Fractint?
by David W. Jones 02 Dec '21

02 Dec '21

Just wondering. https://en.m.wikipedia.org/wiki/Collatz_conjecture --- David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com Sent from my Android device with F/LOSS K-9 Mail.

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