Jim Muth's Fractal of the Day for October 27th, 2002

Jim Muth's commentary for the image:

Fractal visionaries and enthusiasts:

In fantastic adventure games, where intrepid armchair explorers venture into computerized worlds of danger, lava pits are sometimes found. These pits of boiling, bubbling molten rock are just one of the many hazards that block the way to the ultimate goal. If stumbled into, these pits can be fatal to the adventurer . . . that is unless he has in his possession a magic charm of some sort that can enable him to survive things that would ordinarily mean instant death and a trip back to the beginning of the game or level.

I mention computer adventure games because today's image reminds me of a lava pit, with bridges of fractal debris spanning the chasm beneath. I promptly named it "Bubbling Lava Pit". No one has yet fallen into the pit, though many have come close.
Hopefully, this pit will claim no victims in the future.

The formula behind the image is based on the golden ratio, where <a> is to <b> as <a+b> is to <c>. In today's case, I took the negative value and subtracted from it half as much of the negative of its squared value, which simply adds the number one to the original value. The result of this trick is a Mandeloid that resembles two partially coalesced Mandelbrot sets. The East Valley area of this figure is relatively undistorted, and that is where I found today's scene.

When searching for a rating, I looked at yesterday's image and compared it with today's. An honest comparison led me to a rating of 6, which is still above average but only slightly.
The render time of around 4 minutes is in line with the worth of the finished result.

Heavy rain fell during the pre-dawn hours Saturday here at Fractal Central, but by mid-morning the clouds departed and the temperature soon rose to 66F 19C. By afternoon, the grass was dry, which gave the dynamic duo the chance they needed to catch up on lost outdoor time. The extra time outdoors made them so happy that they almost forgot to ask for food when they returned inside.

It's now Sunday morning. We made it through Saturday with no unexpected disasters and a minimum of work. Hopefully, today will be a repeat. Until next time, take care, and then have a little fun.

Jim Muth

PAR file `` Bubbling_Lava_Pit { ; time=0:04:41.27--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.53827492985745600/-0.008649815721493\ 01/90565.23/1/30/3.72648166421796212e-008 params=1/-1.618034/-0.5/-2.618034/0/0 float=y maxiter=600 inside=0 logmap=60 periodicity=10 colors=000uTNvRJwPGxNCyL9yK6vI7tH7rG7pF7nD7lC7jB7h\ A7e88c78a68_58Y38W28U18S08U1Cc2Fm3Iw3Lz4Oz5Rz6Uy6X\ x7w8cv9fu9itAlsBapCemDUlEViF5fGWcHVbJUaLUaOTQS_S\ SZURZXQYZQXPWbOWeOVgNUiMUkMWmLYoKpJarIcsIeuHgvGi\ xFkyFakPSYZJKhVXnehtjarnVprOnvHlzAjxDivGhtJgrLfpOe\ oRemTdkWciZbgafcadfbhkZZnYYpYRrTLsOFtJ9uFDuGHu\ HLuHPuISuJWuJ_uKcuKfuLjuMnuMruNuuNmfYjgVhhTfhQciN\ ajL_jIYkFVlDTlARm7On5Mn2Ko0Iok8ngCldFkJiYMhVPgUQe\ URcTSaTS_STYSUWRVURVSQWQQXOQXNVYO_ZPc_QhRmaSqbTvc\ UzdVyaXx_YwYZvVuTatRbsOcsMerKfqHgpFhoDjnAkm8lm6mt\ 5qmCgJLGIiDJlBJnDLoFNoHOpJQpLRqNTqOUqHecBpQDnTFlV\ HkXJiZLhNfcPeeQcgSaiUkWZnYYp_WraVtcTvdSxZOvTKtNG\ rHDqB9o55m02l44e86ZC8SGALJBFKFFLJFMNFNRFOVFPZFQbFR\ fFSkFSlFQmEPoDOqCNsBMuALw9Ky8Jz7Iz6Hz5Gz4Fz3Ez2Dz1\ Cz0Bz0IzGPzVVziPz_KzROzOSzMWzJ_zHczEgzCkz9oz7kz6gz\ 6cz6_z5Wz5Sz5Oz4Kz4Gz4szN }

frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-abgh)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k((a(z^b))+(d(z^f)))+c, |z| < l } ```

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.

Max Iter's Fractal Follies for October 27th, 2010

Roger Alexander's commentary for the image:

Today's fractal is a remix of my Oct. 24 post. Same formula and palette, different parameters. Like the Oct.24 post ready made at http://maxitersfractalfollies.blogspot.com

Roger Alexander

PAR file Twilight_Remix { ; fract484.gif ; blank ; calctime 0:17:07.88 ; created Oct 26, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-1.89610111352240000/+0.00222840388810970/9616.574/1/22.49999\ 99999827232/-2.86882184674652763e-011 params=4/2/1/60/3/0 float=y maxiter=1500 inside=0 proximity=1 outside=fmod decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; 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 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) 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.

I lost the password to the original account which posted the 2D slices of quaternion newton fractals. For this one it's in 3D and brightness is replaced with transparency. The equation in the image is z^3-1 with a=1+i+j+k. You can see the equation in the UI for the video.

Mandelbulb3D, Photoshop & Lightroom

answering your question u/SeaAuthor3588
it's just a distorted julia set... looks dope

does anyone recognis- erm...

this isnt the full integration its just the finite detail of it.

I usually only need 100k itterations but this needed 3 million and as you can see on the right it still needed closer to 8 million to get rid of the voids

You all share so much good stuff!

I played with fractals in my 20s and understand the generation concept marhematically, but rendering back then was such a hog!!

My comp at the time would go hot and my fan would be at max, and the screen would just be hangin…

So I wanted to post this note of appreciation.

Love youre using your power to share these computationally intensive renders! Amazing how comp power and speed has made these strides and happy to keep watchjng and supporting in the future…

Think fractals are somehow involved in base reality (whatever that might be or if the concept makes any sense with what we know physically).

🙏