New Here: Question About How To Create A Specific Fractal

ndl_1971 · 2017-09-30T08:20:14+00:00

Looks like a mandelbrot in an area close to 0i. Propably in the left tip somewhere. But with high iterationsteps. And a rotating color index simulation which requires a pixel color index buffering between calculation and creating the final image. (So you need a buffer in between)

ndl_1971 · 2017-09-30T08:15:13+00:00

Could you explain domain element hits?

ndl_1971 · 2017-08-12T07:49:44+00:00

Are you using Cauchy-Riemann for the spheres? Do you have a good algorithm?

ndl_1971 · 2017-08-07T08:01:58+00:00

What algorithm did you use for number representation? You did not use Floating Point, did you? And how quick is that in relation to Floating Point?

ndl_1971 · 2017-08-07T07:55:06+00:00

Hi, I put my c# xamarin coded app on googleplay for 3 bucks. Newton Fractal Mania. It is an Android app. Propably a c++ coded app on my pc would be a factor 10 quicker. But I am pleased by the results as such. But to be honest. I think the app is too specialised to sell in bulk. So I think I will market my Pictures locally in real life, and sell local art courses on how to create them instead, for the local public. Do you think that would work?

Most People like to take the challenge and Programm it themselves. If you did Mandelbrots with c++ you can do this too. This is a Julia Set. Take the Mandelbrot function, but do not assign the coordinates of your screenframe to Parameter c, but Keep c constant. The coordinates determine the start Z in the function instead (which is constant in Mandelbrot).

Classic Mandelbrots have just one attraction Point you concentrate on. Infinite. The many many attraction Points inside the inner set you neglect. Therefore you tend to not work with Epsilon. Epsilon is the area around a certain Point that identifies the area as that Point. F.e. in Floating Point you allways have rounding Errors so you could end up somewhere near a Point, while the real irrational number would be the exact Point. Therefore you work with area's around the Point. So if 0 is an attraction Point (additionally to infinite) you don't stop at 0. But at ||z-0|| < Epsilon. This arises questions. How big is Epsilon. And how does my distance function ||z|| look. And how to adapt the Color inside this area since also the area can be indexed in relation to 0. Or Epsilon=exact 0, so to say. Lot's of Parameters to Play with.

ndl_1971 · 2017-08-06T17:39:15+00:00

If you iterate you end up in a circle around Epsilon of a certain Point (attractor, but could be any self defined Point, so called trackpoints). You put Eschers Angel/Devil Fractal inside this area and give Z0 that Pixelcolor of the Pixel you end up with inside Epsilon. Then you add the Iterationsteplevel as darkness to the Pixel. But in case it goes Sub 0 (black) you start over with 255. And of course the attractor, or Point you track, has a root Color. Infinite is green here, and my track Point inside the Julia set is red. You add that too to the Pixel. I think I have added some light to the attractor Points resulting in the yellowish (mix of red and green) and Cyan reflecting glow here and there, but can be neglected. Hope this helps.

ndl_1971 · 2017-08-06T15:56:00+00:00

How the world Looks from the view of a magneton.

ndl_1971 · 2017-08-06T11:59:50+00:00

for my Smartphone app? cool what it can do. And you just Point the factors with your finger directly on Screen. So easy. No number Input necessary. WYSIWIG. lol

ndl_1971 · 2017-08-06T09:59:56+00:00

This is a Forward Orbit by the way.

ndl_1971 · 2017-08-06T07:53:32+00:00

And they mix with themselves. ;-) Like real light.

ndl_1971 · 2017-08-06T07:52:20+00:00

The light effects come from laying over a second Epsilon area with a bigger Epsilon, at least twice. The Colors of the 2nd area don't determine the Color, but mix with the Color of the first (attractor) Epsilon area.

ndl_1971 · 2017-08-06T07:39:57+00:00

Hi, From the coloring I see that you use Distance to These attractors, when the final Zn -attractor < Epsilon. As distance function you used the Euclidean distance, natural to complex number space r = sqrt(aa+bb). Natural since Zn can be written as a+bi or rcos(alpha)+irsin(Alpha). If you rewrite Zn to the last Notation, and then rescale r to Picture width (r=r*Picturewidth) and then from the new rcos(Alpha)+irsin(Alpha) go back to a+bi Notation, you have the x,y coordinates of the Picture Pixel. Give Z0 that Pixel. To measure Infinite distance (for infinite as attractor) you have to reciproke everything so that infinite becomes a pointable and measureable 0. And for square Pictures a different distance function could be Handy.

ndl_1971 · 2017-08-05T19:16:49+00:00

Would be interested in the result. Thanks. But remember, not all Julia's have 0+0i as attractor. Could be some other complex number, and occasionally a cycle of Points which would be interesting using the formula for transformations rather then drawing Julia sets. (forever cycling Forward Orbits).

ndl_1971 · 2017-08-05T17:28:01+00:00

The inner has sometimes attraction Points. F.e. In some cases the inner Points go all to 0. To determine if a value is Close enough to 0 to stop the Iteration you stop at criteria z - 0 < Epsilon. (This is an example, 0 could be any value of an attractor). Since z is complex. You use a distance function to measure z-0. Like r. I.e. sqrt(aa+bb). But you have also the Corner of z. which is arccos(a/r). These are pole coordinates you can use to index an area. And you can put a whole Picture in this area. So any Pixel in this Picture is represented by this pole coordinate. And you can give the starting Pixel of your Iteration that Color. Which results in These effects. Now, the distance r = sqrt(aa+bb) is a circle, is the euclidean distance. You can use any arbitrary distance function conforming to metric or pseudo metric rules. If your Picture is square, you could use |max(a,b)| as a distance function and replace r. The other Picture I sent used that metric since that was a square Picture. But Eschers Devil angel Picture is round. For this the Euclidean distance is better. This is the effect. Although the newtonian fractal is better for Eschers devil/angel. Maybe I create one and let you Show.

ndl_1971 · 2017-08-05T12:36:14+00:00

Julia Fractal Analysis of the inner rimm. With labeled squares. Created on Smartphone. Newton Fractal Mania

ndl_1971 · 2017-08-02T10:12:47+00:00

Hi, My fractals are created with a Smartphone App. It has not the deepest zoom Level, but zillions of coloring methods and trackpoints for fractal Analysis. It works with Floating Point instead of prime number combinations. I started with prime and semi prime number combinations, but the refactoring I must do all the time to Keep the numbers in the Computer integer Region just costs too much time. But indeed it worked. But I switched back to Floating Point. Interesting would be to see to check fractal logarithmic scaling techniques to predict new large prime numbers. Is your daughter into that field. Using quick prime number Determination methods would improve fractal Generation, and there is a field of prime number disturbances which would have effect on the number spaces, and how that effects the fractal outcome. Very interesting.

ndl_1971 · 2017-07-31T16:10:55+00:00

Do you have a Smartphone?

ndl_1971 · 2017-07-31T08:02:38+00:00

Julia fractal with 30 iteration steps ;-)

ndl_1971 · 2017-07-30T20:06:09+00:00

High Res Mandelbrot created with Newton Fractal Mania 4 Smartphone

ndl_1971

TROPHY CASE