no bot or extension, just me :)

Fractal: Gahbrot (p,r) = (4,2) Resolution: 8K Location at: (-1.747297120, 0.000013038) Zoom: 4*10^-5.3 Repeating Color Interval: 50 Color: PiYG Iterations: 1000

After Generating the Logistic Mandelbrot Set, I played around with the formula to get the Logistic Buffalo Fractal
```c++

// zr starts at 0.5 instead of 0.0

temp_zr = fabs(

(-(-zi * zi) * cr) - 2.0 * (-ci * zi * zr) - (cr * (zr * zr)) + (cr * zr) + -(ci * zi)

) + cr;

zi = fabs(

(zi * cr) - 2.0 * (zi * cr * zr) - (ci * (zr * zr)) + (ci * zr) - (ci * -(zi * zi))

) + ci;

zr = temp_zr;

```

Rendering this cost me 3°C of global warming.

4K images: https://blood2oo1.github.io/fractals/gallery/09/index.html

Credibility is achieved!! The p-value numbers are in. Anthony of Boston real time predictions of escalated rocket fire by observing the planet Mars are now confirmed as statistically significant

https://anthonyofboston.substack.com/p/for-six-consecutive-years-anthony

• Probability of Accuracy (2020–2025): The p-value for Anthony’s predictions being accurate is approximately 0.0013, indicating a statistically significant (p < 0.05) probability that the Mars/lunar node phases predict higher rocket fire. Anthony was accurate in 5 out of 6 years (2020, 2021, 2022, 2023, 2025).
• Historical Probability (2005–2025): The p-value is approximately 0.0364, also statistically significant, with 13 out of 21 years showing >50% of rockets fired during Mars/lunar node phases.
• Accuracy Assessment: Anthony’s predictions were highly accurate, as the concentration of rocket fire during Mars/lunar node phases significantly exceeded non-phase periods in most years, particularly 2020–2023 and 2025. Though 2024 was an exception (45.36%), the predicted period for 2024 (Apr - Jun) still managed to capture a critical escalation when Iran launched its first direct military assault on Israeli territory on April 13th 2024, launching over 300 drones, cruise missiles, and ballistic missiles within the prediction window. Overall, the parameters show robust historical and real-time predictive power, supported by statistical significance.

If you want to see what Im exploring check out this prompt.

Vorticism cursive Glyph:: sigil cursive cyrillic calligraphy punctuated Sumi-E adinkra Op Art unknown symetries

If you take that prompt, and put it into an image generator then select the most novel image within 4 or 5 regenerations then put the image in as part of the prompt sometimes depending on the generator used you get images that continue to evolve significantly instead of just getting locked down into a small number of strange attractor states.

Let's imagine something simpler. Let's define the fractal as the prompt

fractal

As far as I can tell the overall properties are maintained in that you can feed in the image it generates, zoom in, or more generally manipulate it. It helps to think of words as like their own dimension

glossy plasma fake Pearlescent map Semicaustic:: Subpixel hidden adinkra:: Half Gaussianoxide weird shading uneven pattern of CMYK cracks bilayer fractured abstract fresco multiple layers difference recursive transparent sigil cursive sign untangled ovoid sprinkle high signal low noise unrealistic shapes made from metallic polished stone spray painted in an amateur style fake enamel sulfurhydride

That prompt doesn't make any sense if you read it traditionally. What you have to understand about image generation when it comes to prompts is that the start and end have significant weight. The stuff in the middle adjusts the details but can feedback in to take control. The words have different weights based on how well represented the word is online.

Oh you can also play around a ton with wordplay keep in mind parts of words are often stored as one token so the word blursed is in a very liminal possibility space. It is blessed, cursed, and blurred all at once. Once you understand that you can sculpt with words its more like balancing an equation then imagining a specific scene.

Morse.EXE glitch geoids corrupted with CMYK oily‑skin smudges, loops of 17‑bit dots, twisted chaos coloring‑book style drawn in MS Paint, punctuated static. 3D convex ovoid sigil rendered in pseudoshape gaussian splatting, subpixel dots biangle streaks over stochastic vector nodes, bismuth dash networked in high‑signal low‑noise, Morse‑code concave scan‑line glitch.txt

Another fun aspect is that you can specify unusual bit depths and it seems to kind of understand what that means. If you use the symbol :: right after a word like this

fractal:: cellular automata

then what you will get is half fractal and half cellular automata assuming it doesnt latch on to cellular but that takes experience.

I feel like this could be a very exciting time for fractals. So much of what is being done uses that recursive magic.

Sadly can't post videos here.

Inspired by this post:

https://www.reddit.com/r/fractals/comments/1mru9yv/37_billion_iterations/

I went to do some exploring of my own.

Using Ultrafractal, I got image 1. That's at the location given by DecentBedroom827, magnification 1e21. Not much further down it gets lost inside that minibrot. Always possible that I could have hunted/tweeked/used more care and gotten deeper, but I think this is a good enough point to stop. It's a pretty picture.

My python program doesn't even use float64, so image 2 is about the best we can get out of it, with a zoom of 100_000_000_000_000. Beyond that, you can crank iterations up all you want, but it won't be able to improve the picture (see image 3)

Start with a rectangle in R^3. For each point in the rectangle, we start the Lorenz system up with that as the initial value, and color the point by the time it takes the system's x value to change sign. I added this one to the examples I distribute with MRaster:

https://github.com/richmit/mraster

You can find it in the examples/3da_frac_lorenz.cpp.

I was just playing around with recursive shapes and thought it would be interesting to add random fluctuations. I like it so much I thought I'd share it.