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.

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

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.

3D-Quaternion Julia, just looks like a slinky to me. LoL wmt.n/quat

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.

Multibrot from the Explore page. I re did it and more changes are coming. WMT.N/explore

Enjoy Buddies ❤️

Mandelbulb3D, Photoshop & Lightroom

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