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Hello, me again.

I thought that i have got the formula for Tetrabrots, but looking at the result i see just 2 Tetra extensions of the main
Body. There should be four.

How to accomplish that ?

Following the formula i used and the result :
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        aa1 = a1 * a1;
        bb1 = b1 * b1;
        twoab1 = 2 * a1 * b1;
        a1 = aa1 - bb1 + x;
        b1 = twoab1 + y;

        aa2 = a2 * a2;
        bb2 = b2 * b2;
        twoab2 = 2 * a2 * b2;
        a2 = aa2 - bb2 + x;
        b2 = twoab2 + z;
 
        aa3 = a3 * a3;
        bb3 = b3 * b3;
        twoab3 = 2 * a3 * b3;
        a3 = aa3 - bb3 - z;
        b3 = twoab3 + y;

        infinitytest = aa1 + bb1 + aa2 + bb2 + aa3 + bb3;  
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    http://www.maverdigitalarts.de/fracts/tetra.jpg (http://www.maverdigitalarts.de/fracts/tetra.jpg)

maverdigitalarts

interesting "slicing" effect; from what (very) little i can tell from that snip, you're doing a 3d escape-time ("infinity") test right? if that's the case, then it looks like your bounding box isn't cubic, so you can expect bits to not be sampled.

Are you sure that each of those "sides" should be the same??  After all, the "top" and "bottom" are different, why not the adjacent sides as well??  Or do you want something that will have all sides to be the same??
 

Hey Paul,

Yes i want the four side symmetry like shown in the drawing below.

Bulbs seems to be difficult to achieve, but the cubics are in the tetrabrot alike formula, but i must have done a mistake, there are just "2 cubic towers", there should be four.

       http://www.maverdigitalarts.de/fracts/BulbyMandel.jpg (http://www.maverdigitalarts.de/fracts/BulbyMandel.jpg)

Hi!

Do you have any suggestion how to correct that ?

Greetings...

hmm if i'm correct about the escapetime guess (confimed?), just enlarge the bounding box so that all 3 sides (cf. only 2) have the same length.

If i have understood correctly, enlarging the bounding box means to decrese the zoom factor ?

I tried it, also set the infinity test to a higher value. with no effect.

Could be a mistake in the formula.

to explain by way of analogy, consider making an image of a (filled) circle. this is just the set { x,y | x^2 + y^2 <= r^2 } so we have a way to check if a point (x,y) belongs to the set, just compare it to our radius given that formula.

let's say we have r = 2, and we test all x and y in the interval [-1,+1]. we won't see the full circle because we're not testing all the points in the circle/disc's domain; what we need to do is enlarge the bounding box so as to test all points that will contribute to the image, in this case by just using the interval [-2,+2] or by setting r = 1.

back to your case: it seems to me from the image you posted that your bounding box isn't cubic - you sample the x and y directions sufficiently, but the z/height is chopped off. i'm guessing this because it looks like there's a clean slice at some z-value, instead of the irregular features seen in the other dimensions.

of course i can't rule out whether or not your formula is incorrect ;) i've never rendered the tetrabrot before.

Hi!

Like i said i am not a Math!     <grin>

Got some extra features  by appliying a dirty trick.

On front side now we have two towers, instead of one like on the sides.

well....

         http://www.maverdigitalarts.de/fracts/TetraCeta.jpg (http://www.maverdigitalarts.de/fracts/TetraCeta.jpg)

PS:
    My images are just Tetrabrot alike achievements
    Original TetraBrot using bicomplex dynamics by Dominic Rochon
    http://www.3dfractals.com/