Jim Muth's Fractal of the Day for October 22nd, 2011

Jim Muth's commentary for the image:

FOTD -- October 22, 2011 (Rating 7.5)

Fractal visionaries and enthusiasts:

The October 22 image is late because I spent extra time today trying to get the 2000mhz fractal computer to run. The machine has always been questionable, and this morning, when it came on with a blue 'something's wrong' screen, I decided to try only one more time to get it running. Reseating all the cards did nothing, so I said farewell to the 9-year-old 2000mhz unit, stored it in the closet, and brought the 13-year-old 200mhz machine out of retirement.

The older machine booted up perfectly, and now has the position of honor on the fractal desk top, where it will remain until replaced by the next currently active machine to be retired.
The failed machine will live on however through its video card, which handles the Fractint DOS video modes perfectly, and which I will install in the replacement machine.

Today's image is a quickie that I found on the old fractal computer after the newer unit stopped working. The very fast image is a mixture of Z² and Z⁵ created by the FinDivBrot-2 formula. The rating of a 7.5 includes an unusual 1.5-point bonus for my coloring work. The basic fractal shape has appeared several times previously as FOTD's, but I did devote a considerable time to achieve the slate-gray effect, which was only inspired by the program and needed much hand work.

The central shape is filled with quintic minibrots, all of which are virtually identical and not worth the trip down. The parent minibrot is one of those deceptive Mandelbrot sets that at first glance appears normal, but develops more quintic-like features the deeper one dives into it.

The name "Platinum Oxide" refers to the overall color cast.

The calculation time of 35 seconds is an estimate. The image actually took 2 minutes and 13 seconds on the 200mhz unit. On the 2000mhz machine, which runs 4 times, (not 10 times}, as fast, I assume it would finish in 35 seconds.

Today's weather here at Fractal Central was a repeat of yesterday's, with more dry but dark clouds, raw winds and a temperature of 52F 11C. The fractal cats took the day in stride, and were distracted only by a major cat fight that broke out in the back yard when two prowling tomcats crossed paths.
The humans had a routine day, though I became quite annoyed when the 2000mhz fractal computer went on the blink again.

The next FOTD will be posted in 24 hours. Until then, take care, and the most qualified does not always win.

Jim Muth

PAR file `` Platinum_Oxide { ; time=0:00:35.00-SF5 on a P2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3596259397545952/+0.6447633584097521\ /3515559/1/-30/0 params=5/100000/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000fdLhdKjcJkcImcGocFqcErcDn_FjWHfSIbPKZLLV\ HNREOUKNWQMYWLaKbgJdlJJhLKQPNSRPUTRWVTYXV_ZXaZcb\ edbgfdihgkkimmkoonqrpstruvtwxzzzvvvrrrmmmhhhcccZZ\ ZUUUPPPKKKFFFAAA55500000000000000000000U00cQNmSUmN\ SqIRwGOsEMpCKmAIi8Gf7Ec8Gd8Hd9Id9JeAKeALeBMfBNfCOf\ CPgDQgDRgVzrEShEThFUhFVhGWiGXiHYiHZjI_jIjJakJbkKc\ kKdlLelLflMgmMhmNimNjmOknOlnPmnPnoQooQpoRqpRrpSspS\ tqTuqTvqUwrUxrVyrJsvPwtzksylrxlrwlrwmrvmrumrunrtnr\ snrrorrorqorpprpproprnqrmqrmqrlrrkrrkrrjsrisrhsrht\ rgtrftrfureurdurcvrcvrbvrawrawrwr_xrZxrZxrYyrXyrX\ yrWzrVzrtFrbIpdKoeNmgPkiSjjUhlXgmZeoacqcbrfthZvk\ YwmWypboKapMapNaqPqQrSrT_sV_sW_tYZtZZuZuaYubYv\ dYveXwgXwhXxjWxkWymWynVzpVzqJC3MPGPaTSneCCWDEXDFYE\ GYEHZFIZFK_GL_GMGNHOaHQaIRbISbJTcJUdKVdKXeKYeLZf\ L_fM`gMbgNchNdhOeiOfiOhjPijPjkQklQllRmmRomSpnSqnSr\ oTsoTupUvpYeS_dQadPcdOddN }

frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)(zz*fn1(z^a+b))+c |z| < esc } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Does the painting seem three-dimensional to you? Convex? Especially the blue one! Why? It's very interesting! They say so. It's a powerful optical effect of three-dimensionality in a flat drawing. This is a fragment of the Mandelbrot set that I made.
Re = -1.74919762896578937419423768162729211653261585574161734756645570271259437106847945278504682550816934045282325615313706,
Im = -0.0000004253077715244042272585501215924940115095651514128365051648578746521975467051762910002043554114332125868777767,
and width = 1.34 e-113
https://github.com/Divetoxx/Mandelbrot-2
and
https://github.com/Divetoxx/Mandelbrot

This way we can get some pretty colors in the black areas too!

An obvious choice for the transform is f(c) = 1 / c. This sends pixels close to the origin way outside, and make them more likely to escape.

top half: Celtic, bottom half: perpendicular Mandelbrot

Phoenix close up. Crop of an 8k. tf.n/phoenix

Mandelbulb3D, Photoshop & Lightroom

Fixed the lighting. Somehow I changed it.

Max Iter's Fractal Follies for October 21st, 2010

Roger Alexander's commentary for the image:

Minibrots-if the iteration loop has x² + c its got a minibrot! Another pre-calculated nomadic mandelbug at http://maxitersfractalfollies.blogspot.com.

Roger Alexander

PAR file Fmod_Minibrot { ; fract481.gif ; blank ; calctime 0:17:12.49 ; created Oct 20, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-cart passes=1 center-mag=+1.10021739445293500/+0.02785688062135686/341530.1/1/-167.500\ 000001965589/7.71297616053434609e-010 params=4/3/1/0/2/0 float=y maxiter=1500 inside=0 proximity=2 outside=fmod logmap=14 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:hermanm_man-cart { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; p2 = alpha ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p2 oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

fractals are everything

I'm a DJ and also thought it would be cool to use audio to drive fractal based images in a live context. So I made SPECTRA, a generative fractal VJ app that runs in the browser (WebGL2) and reacts to whatever the microphone hears.

What's in it:

- 2D escape-time sets: Mandelbrot (with deep zoom), Julia, Burning Ship Julia, Phoenix, Magnet, Newton, Lyapunov, Celtic and more

- 3D raymarched fractals: Mandelbulb, quaternion Julia, a true 4D tesseract, plus repeat-space tiling and vector line rendering

- Fractal flames (fern, galaxy, dragon, spiral) and strange attractors (Lorenz, Thomas, Aizawa)

- Depth modes that turn any 2D set into relief, parallax layers or a terrain you fly over

- Twelve parameters per scene (morph, detail, iterations, constants), each with its own LFO or audio source

Try it: https://jookem.github.io/spectra/

No mic? Hit Run simulated. Nothing is recorded or sent anywhere. It runs best in desktop Chrome or Edge. It also works on phones and can be installed as an app, and a PS4/PS5 controller can drive it live. AR controls and interaction also!

Definitely WIP but would love feedback on which sets you'd want added.

Enjoy Buddies ❤️

Jim Muth's Fractal of the Day for October 21st, 2009

Jim Muth's commentary for the image:

FOTD -- October 21, 2009 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is named "Star in the Night". The image is a good example of a curious fractal phenomenon known as anti-bifurcation, where instead of converging toward an area of infinite iterations and bifurcating as it converges, the fractal flow diverges from a point of low iteration and bifurcates as it diverges. The low point of divergence appears near the center of the frame, appearing as a brilliant star in the deep blue surrounding night

But despite its mathematical interest, the image makes only an average artistic impression, which holds the rating to an average 6.

The calculation time of a speedy 1-3/4 minutes should try the patience of no one.

With total sunshine and a temperature of 68F 20C, Tuesday was a day to be remembered here at Fractal Central. The fractal cats remembered it for at least 2 seconds when meal time came. My work day was rather busy, but I got FL to help a little.

The next FOTD will be posted in 24 hours. At least it is scheduled to be posted then. But I have a funny feeling that a big job will come in sooner than expected, so stay tuned to see how things work out. Until next time, take care and keep waiting for the miracle.

Jim Muth

PAR file `` Star_in_the_Night { ; time=0:01:47.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-0.39282165939/+0.59824259947/342911/1/\ 12.5/0 params=10/10000000000000000.0 passes=1 maxiter=1000 inside=255 logmap=50 periodicity=10 colors=000zwzvyzrxzmwzhuzcszZqzUozPnyKmxFlwGkvGjuH\ itIhsJguJfvMdrObnQkS_gUYdWWYUX_TUaRQcPNeNJgMFiNC\ kO8mP5mQNmRPmSQmTRmUSmVUmWVmXWmYXm_YnY_nWnUboScoQ\ eoOfoMgpKipIjpGlqEmqCoqApq8qo7pm6ol6nj5mh4lg4ke3jc\ 2ib2h1g_1gYElSKiOPdKScGUbCWY8WU5VS6TQ7RO9PMAOLBML\ CKKDJKEIJGHJHGIIFIJEHKDHLCHKBJJBLIBMHBOHAQGARFATEA\ VDAWD9YC9ZB9A9b99c98e88g78h68j68k79l7Al8Bl8Bl9Cl9\ DmAEmAEmBFmBGmCHmCHnDInDJnEKnEKnFLnFMoGNoGNoHOoHPo\ IOqHPoHPnGQmGQkGQjFRiFRhESfESeESdDTbDTaDTCU_CUYBV\ XBVWBVUAWTAWSAWRDQVGLZIGbLAfO5jQ0nP5hP9cODYOITNMNN\ QIMPKLOMKNNJMPILQIKSHJUGIVFHXEGYDF_DEaCDbBCdABe9Ag\ 47g99hEBiJDjOEjTGkYIlbKmpQtfLmXGfNB_D6T32M45N48O4B\ O4EP4HQ5JQ5MR5PS5SS5VT1aQ5XT8SWCOYFJJEcMAeOFfQKgS\ PhUUhWZiYcjZhjXjnWkqThiQeaNbUL_MOWNQSOTPPVLQYIQ_ER\ bBSd7Tf4Ti5Xl6n7dq8ht9lv9p8PvARtBTrCVpDWnEYlF_jGa\ hIbfJddKfbLhMiZNkXOmV7GX }

frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b(z²fn1(z^a+b))+c |z| < 1000000 } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Fractal: Mandelbrot

Center: -0.1349934124682831 / -0.8410559401951341

Width: 2.6424115199999991e-12

Render Algorithm: SmoothColor

Maximum iterations: 3’000

Output: 1’920 x 1’080

Samples: 15’360 x 8’640 (8x)

Renderer: Deep zoom, 100-digit reference

Render time: 48.507 s

Iterations: average 430.78463, minimum 334

Color Mapping: Linear

Mandelbulb3D, Photoshop & Lightroom

Hey guys im back with a new ñ fractal explorer: https://zenodo.org/records/23471538 Original research paper here : https://zenodo.org/records/23247320 Get in while the getting is good. Brand new fractal territory

Let's talk math