Doug Stewart <Dastew@sympatico.ca> wrote: To: "Fractint and General Fractals Discussion" <fractint@mailman.xmission.com>
Jonathan Osuch wrote: <snip>
So, instead of plotting: for (row=0, row<ydots, row++) for (col=0, col<xdots, col++)
we could plot: for (theta=0, theta<360, theta++) Or something similar.
<snip> Back in th 1980s I wrote a program that drew some very nice pictures similar to these ideas. you need: starting x and y ending x and y number of points in between number of iterations at each point. I also had the colour changing for each iteration at the point. If someone would add this to fractint I am sure that it would be a hit.
If you choose the line properly you get very stunning pictures.
Right you are, Doug. Take a look at the image generated from the included FRM and PAR. These simply draw a pentacle through the main cardioid of the M-set with corners at the 0,1/5,etc. bud tangencies, and then render the points using the passes=o. I didn't have any idea that a "knot" of such complexity could result from such a simple shape! Do you remember the settings or general algorithm you used in your program? I am very interested in these slices of the M-set orbit image object, and if you would share your experience with these I'm sure others would appreciate it as well. ---Hiram /* PAR: Flower_Antiflower */ Flower_Antiflower { ; ;HiramBerry;1280x1024 with maxit-orbitdelay=100;resolut ; ion affects color with passes=o,outside=summ, so adjust ; difference according to density, eg. maxit-delay=56 for ; 1024x768 or 37 for 800x600. reset=2004 type=formula formulafile=orbit.frm formulaname=morbcardpentanglin passes=o center-mag=0.103851/-0.0106518/1.315817/1/-90/3.88578058618804789e-016 params=0/1/1/5/2/5/3/5/4/5 float=y maxiter=300 inside=0 outside=summ periodicity=0 cyclerange=1/1 orbitdelay=200 colors=mmwxZU<5>_NHVLFRJDMHBIF9<3>070<108>0x00x00y00y00z0<126>000 } /* FRM: Morbcardpentanglin */ Morbcardpentanglin{ ;HiramBerry; passes=o,orbitdelay=nonzero. Domain points ; drawn from the segments connecting the vertices of a pentacle, iterating ; from them. Iteration is Mandelbrot style,p[1..5]=vertex[1..5],no z-perturb, ; vertices specified by (increment(int),period(int)) point on main cardioid. IF(initialized==0) initialized=1 rays=10 cols=real(scrnmax),rows=imag(scrnmax),pts=cols*rows rctx2=floor(pts/rays)*2 theta1=2*pi*real(p1)/imag(p1),rad1=(1-cos(theta1))/2 theta2=2*pi*real(p2)/imag(p2),rad2=(1-cos(theta2))/2 theta3=2*pi*real(p3)/imag(p3),rad3=(1-cos(theta3))/2 theta4=2*pi*real(p4)/imag(p4),rad4=(1-cos(theta4))/2 theta5=2*pi*real(p5)/imag(p5),rad5=(1-cos(theta5))/2 v5=0.25+rad5*(cos(theta5)+flip(sin(theta5))) v1=0.25+rad1*(cos(theta1)+flip(sin(theta1))) v2=0.25+rad2*(cos(theta2)+flip(sin(theta2))) v3=0.25+rad3*(cos(theta3)+flip(sin(theta3))) v4=0.25+rad4*(cos(theta4)+flip(sin(theta4))) r12=v2-v1,r13=v3-v1 r23=v3-v2,r24=v4-v2 r34=v4-v3,r35=v5-v3 r41=v1-v4,r45=v5-v4 r51=v1-v5,r52=v2-v5 bailout=4 ENDIF pti=imag(scrnpix)*cols+real(scrnpix) disti=floor(pti/rays),rayi=pti-disti*rays z=0 IF(rayi==0) C=v1+(disti*2+1)/rctx2*r12 ELSEIF(rayi==1) C=v1+(disti*2+1)/rctx2*r13 ELSEIF(rayi==2) C=v2+(disti*2+1)/rctx2*r23 ELSEIF(rayi==3) C=v2+(disti*2+1)/rctx2*r24 ELSEIF(rayi==4) C=v3+(disti*2+1)/rctx2*r34 ELSEIF(rayi==5) C=v3+(disti*2+1)/rctx2*r35 ELSEIF(rayi==6) C=v4+(disti*2+1)/rctx2*r41 ELSEIF(rayi==7) C=v4+(disti*2+1)/rctx2*r45 ELSEIF(rayi==8) C=v5+(disti*2+1)/rctx2*r51 ELSE C=v5+(disti*2+1)/rctx2*r52 ENDIF : z=sqr(z)+C |z|<=bailout }