Title: newton 3d+ new formula and picture Post by: ericr on January 10, 2016, 04:30:18 PM test for a 3d newton
I waiting the critiques , I m not sure to have done a real newton fractal (I only hope so) (c+sin(x))/cos(x))- x on deviant art a wonderfull newton 3d has be done , I try do the same but it is very very hard !!!!!! (if your alone) Title: Re: newton 3d Post by: JosLeys on January 16, 2016, 08:54:07 AM Your formula is not for the Newton fractal.
Look here first: https://en.wikipedia.org/wiki/Newton_fractal Here is a page of 3D Newton fractals done in Ultrafractal: http://www.josleys.com/show_gallery.php?galid=338 Title: Re: newton 3d Post by: ericr on January 16, 2016, 12:54:33 PM sorry, yes the formula was worng !
It's z-c*f(z)/f'(z) but in 3d i must do x':=x*cos(a)sin(b) y':=y*cos(a)cos(b) z':=z*sin(a) and x=x-c*f(x)/f'(x) y and z the same I make a new jit formual but it s not the god fractal result ???? Title: Re: newton 3d Post by: ericr on January 17, 2016, 04:27:11 PM my last version of newton 3d
after help of jesleys but the result is not ok no:=sqrt(((x1-x)*(x1-x))+((y1-y)*(y1-y))+((z1-z)*(z1-z))); ed:=-k*((1-exp(-m*no))/(1+exp(-m*no))); Piteration3d^.Rstop:=ed; this parte calcul the DE using -k*(1-exp(-mED))/(1+exp(-mED)) Title: Re: newton 3d+ new formula and picture Post by: gannjondal on March 01, 2016, 11:38:15 PM Better later than never, Eric :) - As discussed in dA here a few more details on my pseudo Newton picture made with an JIT formula. I wanted fast results, honestly, and ignored any mathematical correctness, and many of the discussions here in the forums (sorry to the community :evil1:). Therefore I have made a very simple approach, and said that 1/(t^p) = t^(-p) also for triplex numbers. The result was better than expected - but actually not 3D. I simply could see a classical Newton in a cut. Nevertheless I want to share. Promised is promised :-) (http://orig05.deviantart.net/8e18/f/2016/061/6/c/newttest_outside_web_by_gannjondal-d9toz0f.jpg) I have attached the formula JIT_gnj_RealPowerPseuNewt3_02.m3f - you can see it's simply a RealPower turned to t(n+1) = t(n)*(p-1)/p - c*[t(n)^(1-p)]/p To be more exact it needs: cut at z=0, coloring = Rout angle x,y, and a map color map with its. trap That's it. Params: Code: Mandelbulb3Dv18{The 'original' picture at dA (http://pre11.deviantart.net/4515/th/pre/i/2016/003/d/7/jit_test_01___pseudo_newton_by_gannjondal-d9mmm6k.jpg) uses a slightly different formula (based upon the IQ bulb formula delivered with M3D v190). If you switch on inside rendering you get some 3D feeling. Howerver it's SLOW and the DE is weird: (http://orig11.deviantart.net/0cbd/f/2016/061/7/9/newttest_inside2_web_by_gannjondal-d9toyyz.jpg) Params: Code: Mandelbulb3Dv18{Last, but not least an overview. At the lower part of the picture below you can see what happens for larger values of z. So the classic picture is there just for small x/y/z. (http://orig04.deviantart.net/6f65/f/2016/061/4/8/newttest_overview_web_by_gannjondal-d9toyzq.jpg) Params: Code: Mandelbulb3Dv18{I have also tried to find a way to either to manipulate bailout conditions (similar as you), or to set x/y/z to values which do diverge when Newton does converge. However, I assume currently that neither params like Piteration3d^.Rstop can effectively be changed during calculation - nor any other variables than x, y, and z can simply be taken over from one iteration to the next one. But well, I was too lazy until now to walk through the M3D source code; and before going to Andreas I would want to make some dedicated tests. // Note to the community: As this is my first forum entry I'm asking you for your pardon for any mistake I have possibly made. // Please feel free to tell what I should correct in style, or wording. Thank you! Title: Re: newton 3d+ new formula and picture Post by: hobold on March 02, 2016, 09:49:55 AM Don't worry, gannjondal, your post is informative and illustrated very well. That would be a good standard even for a 1000th posting. :)
Title: Re: newton 3d+ new formula and picture Post by: ericr on March 02, 2016, 10:05:15 AM Thx very much and thx for all formulas and deviantart Eric |