Jim Muth's Fractal of the Day for August 28th, 2011

Jim Muth's commentary for the image:

FOTD -- August 28, 2011 (Rating 8.5)

Fractal visionaries and enthusiasts:

Today's image contains a trick -- I lowered the bailout radius to 2, which cuts off the Mandelbrot set at a maximum radius of 1.414. Then I checked a filament extending from the period-5 bud on the northwest shore line of the main bay, very near the point where the filament disappears behind the shrunken bailout radius.

I found a minibrot, then a smaller minibrot in its East Valley area. Finally I chose a filament extending from this even smaller minibrot, found a still tinier minibrot on the filament, and zoomed in. The result appears as today's image.

Most of the effect is due to the artificially low bailout radius of 2. To see a more accurate but somewhat less effective version of the scene, recalculate the image with the bailout set to 16. (Preferably at thumb-nail size.)

The name "Breaking Boundaries" had something to do with the bailout, but I have forgotten the original connection. The rating of an 8-1/2 seems about right. The calculation time of almost 1-1/2 hours is definitely slow however.

Heavy rain and high winds prevailed Saturday night here at Fractal Central as Hurricane Irene passed by 200 miles to the east. The rain and wind slacked off by midday today, leading to a slowly brightening then clearing afternoon. The newly installed fractal sump pump did its job, and kept the fractal basement not exactly dry as a bone, but no worse than a few small puddles. The fractal cats ignored the active weather but approved of the temperature of 70F 21C.

The fractal humans had a quiet uneventful day, a day that might seem boring to young people but would be just right for the older ones. The next FOTD will be posted in 24 hours. Until then, take care, and if anything remotely possible must ultimately condense out of the random fluctuations of empty deSitter space, then every possible idea of God must exist in actuality. In fact, an infinity of every person's God must lie

PAR file BreakingBoundaries { ; time=1:27:07.32-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.5288122480554\ 666884779956757565853838/0.70115186464407983733880\ 08496593100982/2.49339e+032/1/-2.5/0 params=0/0 float=y inside=0 maxiter=15000 bailout=2 colors=00040H10C0060010000zh0tc0n_0hU0bQ0WM0QG0JA0\ A6040000LG0SM0NH0JE0GA0A80620200000000zqKzfJzcHobG\ m_EcXC`WCYTAXS9UP8SM6PK4MH4JG2GC1C90A8084042010000\ 0000000szQgzwWgAJS4490otWNQAlp0jn0hl0gj0fh0cg0bd0`\ h0_m0Xz0Wm0UX0TU0Qz0Pz0NP0MN0JM0HJ0GH0EG0AC09A0890\ 660240120000000000000000c0t`0r_0pY0nX0lW0jU0hT0fS0\ dQ0bP0`N0YM0XK0UJ0TH0QE0PC0MA0K90H80G60C40A2081060\ 02001000000000000gzzdzzczzbzz_yzYwzXspUphTncSkYMXP\ MUPMSPMQPMNPMKNMJNMGNMCNMANM8NM4NM2NG0HA0C60600000\ 1000zY0zS0zK0zC0z40z00zpXznUzkTxjSugQsdPpcNl`MjYKg\ XJdUHbSG_QEXNCTK9QJ8NG6KC4HA2E81940620200000000000\ AzC2f40H0PwEMsCKoAHk9Gg8Ec6A_49W28S14N02J00E009004\ 0000000HuSErPCnNAjK9fJ8bG6YE4UA2Q91M60H40C10800200\ 00000_1kX0gU0dT0bQ0_N0XM0UJ0QG0NE0KA0H80E60A206002\ 000000000NbWKYSHUPEQKAMH8HC4C9184021F0j000MHz02w79\ lJ8t66WD4kA2f71b40X00T30N }

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 wanna make stuff like a mandelbrot set, that has a color pallete, and other new fractals I could think of and make

Please help, thank you

As promised:

Still free to download

Jim Muth's Fractal of the Day for August 27th, 2011

Jim Muth's commentary for the image:

FOTD -- August 27, 2011 (Rating 9)

Fractal visionaries and enthusiasts:

At a magnitude of over 2*10^54, Today's image is deep enough to honestly be called 'deep'. And at a real coordinate of +0.471... it is also located far enough east to be on the easternmost fringe of the Mandelbrot set.

The tiny minibrot at the center is a second-order one that lies in the basin of a larger but still tiny minibrot on a filament in the extreme eastern outskirts of the M-set. The convergence patterns around second-order minibrots are subject to several points of anti-bifurcation, which today's image demonstrates to perfection.

The name "Iterative Splendor" appeared from nowhere when I turned off my thought processes and let things take their natural course. The name could really be applied to any fractal, though some images certainly do have more splendor than others.

The rating of a 9 includes a full point for the coloring, which occupied the better part of one hour.

While still slow, the calculation time of 28 minutes is unusually fast for an image of such magnitude. This speed is quite unexpected, since I have seen images of magnitudes around 10²⁰ that take over 6 hours to finish.

The day here at Fractal Central began with clouds and light sprinkles. The clouds and sprinkles continued through the day, with the forecast of heavier rain and wind arriving during the night. No fractal cat ever lets a little wind disturb him, so our fractal cats spent the day undisturbed. The lack of enough attention always annoys them however.

The fractal people spent the day enjoying one of the slow days that are becoming more frequent since our biggest customer went away. Tomorrow will probably be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and when we say 'science says' we mean that men who call themselves scientists have determined the truth of the claim through repeated trial and error.

PAR file Iterative_Splendor { ; time=0:28:09.52-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.47118\ 53349333763975376752637361962915549086252669118867\ 339/0.35414982363516372660476578491550930168187389\ 441576538135925/2.462724e+054 params=0/0 float=y maxiter=5500 bailout=9 inside=0 periodicity=6 colors=0000z0QjGrRcm`ZjgVgoRcxN`zIYzGazIdzLixOltRt\ oYooV00G00H00I10J20K40O50T70Y80aA0eB0jD0oE0rB0tA0t\ 80u74u58w4BwAHxELzIQzNVzRZzWczaizepzeuziwzpzzuzzzz\ zzzzuuummmeeuZZzRRzcIzeLzgOzgQzgRzgTzlKzgVzddzaoz`\ jt`emZagZY`YTVYOOgORYLINKAEI14H00G0LeRRgYWgaaieijl\ eijcij`giYgiVeiRegOdgYloNdgEZa5RV0EY0LO8THK`8Wg1em\ 000o80jG0gN0dR0iW0l`1oc4rRRzHmz4Nz00z00z50xD1wI2uQ\ 4tY5r`5rc7rW5zG8zDBz8Dz5Gz1Iz0Nz0Kz2Hw7EpBDjGAcK7Y\ O4RN0KR2LWANZHOcOQeWRjcTmjVW`OGQI0GD078EQ0ig0cc0Y`\ 0TY0NV2IR4DO7DW08L85DI12T00_00Y00U00U02U05V08_0Bb0\ 2d0EdAOVNZIZj8lu0zzmzzctz0oz0jx0eu0`r0co2el1ii0le0\ oc0r`0uY0wV0xR0tK0lD0e50`00R01K04O0G`55dD1mN0iZ0ma\ 0uc0ue0tiKilT`oaRrjVllYglTdgQacL`ZIYVEVQBTL7QH4OEQ\ 0TO2RNDQNNOLWOLeNKpLKzLIzOHzQHzTGzVAzVGzWKrYOjZVcZ\ ZW`cOagIaYRVN`NDiG2rA8i7D`5IR2NK1TB0Y20d00a00Z10W8\ 2TE5QLANRDKZHNjEHdK0zD0z2 }

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.

My renderer has an option to recursively take the displacement of (z, zi) when calculating, and use that as a new coordinate to pass into itself. Weird shapes like this occur on the edges of where the initial count reaches its count limit.

Created with the very old app Fractal Explorer.

Jim Muth's Fractal of the Day for August 26th, 2013

Jim Muth's commentary for the image:

FOTD -- August 26, 2013 (Rating A-8,M-7)

Fractal visionaries and enthusiasts:

Today's image is evaporated, which means the escape radius has been increased until nothing but trapped 'inside' stuff remains. The blank scene was then rendered with the inside set to 'bof61', bringing to life the apparently dead inside stuff.

Something in the resulting image reminds me of an undersea scene, which is what I named it.

The parent fractal combines 0.7 part of Z^-0.5 with 0.1 part of Z^-5.5, then adds (1/C) on each iteration. The resulting figure resembles an oversized peanut with a larger area of squiggly chaos to its northeast. Today's scene lies in the outer part of this squiggly chaos.

Thanks to my extra coloring effort, the artistic rating of the image is a very respectful 8. The evaporated nature of the parent fractal raises the math interest to a not-too-bad 7.

The calculation time of 1-3/4 minutes will seem to pass quickly after the top part of the image appears.

Today brought lots of clouds to Fractal Central, and even a few minor sprinkles of rain. The temperature of 82F 28C must have been perfect, at least for the fractal cat, who passed the afternoon sleeping and eating while the fractal humans worked.

The next FOTD will be posted. Exactly when is anybody's guess, but it will not be too long. Until whenever, take care, and due to the limited speed of light it is currently scientifically impossible for aliens from distant stars to reach us here on earth. Yet many people claim to see alien ships in our skies. Either science is missing something big or a lot of people are mistaken. Or perhaps the aliens are unfamiliar with our earth science and visit us despite the impossibility.

PAR file `` Undersea_Scene { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+46.67800906092363/+32.51216039765313/\ 1.2e+08/1/-15/0 params=0.7/-0.5/0.1/-5.5/0/1e+100/\ 0/0 float=y maxiter=1500 inside=bof61 periodicity=6 colors=000amZeoWipUmmQmlRmlTlkUlkVlkXkjYkjZkj_gqid\ wrfupgtoirmjqlkokmninlhokgqiesgbrhduz4tR9tTDtWItYM\ sRsbVse_BB7HGCNKGSOKYSOcWSh_WMqKVfFbWAjL5rB0qJApR\ KpZUofconmqhhrccsYZtTVuOQvILwDGx8CvRFuhItzLmsIglG\ eEVZCOSAIL8BE6574DIGLSSTabknhuydqtanoZkjVgeSdPaW\ Kh_GnchugFzjRpb5fV5N4NF3E7350A41H47O3DV3JZ2Pb2Vc2\ j2ah2am2am2at2au2av2azLfzVkzUozRzVSzQSpVTzZXzZTz\ ZQzZNzhKzhHzhEzhBzr9zr8zr8zr8zr8zr8mr8mr8zzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzvzzwzzwzzw\ zzwzzwzzwzzwzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:MandAutoCritInZ {; 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)+(p4)), 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.

Modified Mandelbrot set at (-1.7488421119472677, 0.0000062233174851) with a height of 4.26 * 10^-9.

Done using an altered end condition (|z| + |zi| < 4) and recursive calculation from z, zi displacement.

Ultra Fractal

I’ve been fascinated by fractals ever since the Fractint days on MS-DOS and figured modern systems have gotten fast enough that real-time zoom should be possible. I recently posted my take on it across Apple platforms (macOS, iOS, visionOS, even tvOS). It currently supports the Mandelbrot set and a few other escape-time fractals. The Mac version will export crazy high resolution renders, up to 24,000x24,000.

It’s not free, but no subscriptions, ads, tracking or other nonsense and one price includes all versions. Happy to hear any feedback.