Welcome to Fractal Forums

Hi
I need help / opinions in fractal formula summations.

Are following names correct?
Is there anything "famous" I am missing (beside Mandelbar / Tricorn / Conjugated)

Here is the list "collected" for the moment:

---

---

---

Mandelbrot
Its formula is Z = Z^2 + C
here is simple code:

static color Z_mandelbrot(float x, float y, color it){
   float zx = 0;
   float zy = 0;

   color i;
   for(i = 0; i < it; ++i){
      float zx2 = zx * zx;
      float zy2 = zy * zy;

      if (zx2 + zy2 > ESCAPE2)
         return i;

      // z = z*z + c

      zy = 2 * zx * zy + y;
      zx = zx2 - zy2 + x;
   }

   return i;
}

---

Burning Ship

same as Mandelbrot, but get ABS of zx and zy:

static color Z_burningship(float x, float y, color it){
   //...
   for(i = 0; i < it; ++i){
      zx = ABS(zx);
      zy = ABS(zy);
   //...

---

Perpendicular Burning Ship

same as Mandelbrot, but get ABS only on zy (imaginary)

static color Z_perpendicularburningship(float x, float y, color it){
   //...
   for(i = 0; i < it; ++i){
      zy = ABS(zy);
   //...

---

Perpendicular Mandelbrot

same as Mandelbrot, but get ABS only on zx (real) and we do it with negative sign

static color Z_perpendicularburningship(float x, float y, color it){
   //...
   for(i = 0; i < it; ++i){
      zx = - ABS(zx);
   //...

---

---

---

Buffalo

Its formula is Z = Z^2 - Z + C

static color Z_buffalo_original(float x, float y, color it){
   float zx = 0;
   float zy = 0;

   color i;
   for(i = 0; i < it; ++i){
      zx = ABS(zx);
      zy = ABS(zy);

      float zx2 = zx * zx;
      float zy2 = zy * zy;

      if (zx2 + zy2 > ESCAPE2)
         return i;

      // z = z*z - z + c

      zy = 2 * zx * zy - zy + y;
      zx = zx2 - zy2 - zx + x;
   }

   return i;
}

Question - how is called same fractal without ABS() ? It looks interesting enough to have name?

---

---

---

Celtic

For these I do not know the complex number formula. It looks like Mandelbrot formula, but have ABS "inside".

static color Z_celtic(float x, float y, color it){
   float zx = 0;
   float zy = 0;

   color i;
   for(i = 0; i < it; ++i){
      float zx2 = zx * zx;
      float zy2 = zy * zy;

      if (zx2 + zy2 > ESCAPE2)
         return i;

      // z = z*z + c

      zy = - 2 * zx * zy + y;
      zx = ABS(zx2 - zy2) + x;
   }

   return i;
}

---

Perpendicular Celtic

same formula as Celtic, but ABS(zx), with negative sign.

static color Z_perpendicularceltic(float x, float y, color it){
   //...
   for(i = 0; i < it; ++i){
      zx = - ABS(zx);
   //...

---

and we have another Celtic variation called Perpendicular Buffalo
same formula as Celtic, but ABS(zy).

static color Z_perpendicularbuffalo(float x, float y, color it){
   //...
   for(i = 0; i < it; ++i){
      zy = ABS(zy);
   //...

Question - Is this correct name? Its formula have noting to do with Buffalo?

---

I will edit the question and add pictures tomorrow

http://www.nahee.com/spanky/www/fractint/fractal_types.html
http://www.chaospro.de/formulas/display.php?fileid=222

HTH

the list from nahee is quite what you are aiming ;)

so, for making a comprehensive list, you should consider making it more detailed, for once you are listing escape time fractals, associating their fractal dimensions to them is very interesting as well ( can be hard to determine ) like this list:
https://en.wikipedia.org/?title=List_of_fractals_by_Hausdorff_dimension


and in fact i think this list can grow quite a lot, like fn(z)^2+c where fn stands for any 1-ary function... how to classify such?

Hi

I never wanted to do broad summarization. I just wanted to summarize well known escape tie fractals such Mandelbrot et all, so I can make a useful webpage where all these are listed along with formulas, so next one not looking alll over the internet for the formulas like I did last two weeks...

Another problem I see is "clasical" fractal naming. Internet is fill with some pictures, where nmes are completly wrong. I can see a picture of something, they name it burning ship, and in a week I found it is celtic or something else. I think such page will be quite usefuf for beginners.

Finally, when I say page, I really mean single html, not whole webasite - just nae, formula and small picture.

Hope now is much clear what i am trying to do?

 :hrmm: this makes me thinking of changing the usage of
http://ultrafractalwiki.fractalforums.com/

to
http://wiki.fractalforums.com/

which should contain detailed informations like you described

Here is what I implemented in Kalles Fraktaler

http://stardust4ever.deviantart.com/art/Mandelbrot-ABS-Variations-Complete-Set-of-Formulas-487039852

And most of these
http://stardust4ever.deviantart.com/art/Cubic-Mandelbrot-ABS-Variations-Incomplete-487039945

excellent idea cK!

@kalles - your images were my starting point, but I found some older versions that had just few fractals.

so lets do the wiki?