http://formulas.ultrafractal.com/login.htm Comment { Formulas created by Evelyn Cowan www.skydakini.com/Fractal_Art.htm Revised 2002FEB10 These formulas are named after my grandchildren. The formulas are fairly simple and seem to work well when using inside and-or outside coloring. Some of these formulas just appear to be faint circles. I don't know if they are real fractals but if one applies some param changes and outside coloring something of interest can be achieved. : ) Thank you for trying them out and please let me know how I can change and improve them. } evcaleb-01 { ;replaces "caleb" ;bailout setting added init: z=#pixel a=2 b=2 c=#pixel loop: z=a*b*z^3+a*z^2+c bailout:|z|<@bailout default: title = "caleb-01" center=(-0.12,0.0) param bailout caption="bailout" default=4.0 min=1e-20 endparam } evCaleb+rsp { ;bailout setting added init: a=1 b=2 c = #pixel if @ca == 0 z=#pixel elseif @ca == 1 z = -2/(3*b) elseif @ca == 2 z= @cut endif loop: z=a*b*z^3+a*z^2+c bailout: |z|<@bailout default: title = "caleb-rsp" param CA enum="pixel" "critical" "user" default=0 endparam param cut default = (0,0) caption = "Cut plane" endparam param bailout caption="bailout" default=4.0 min=1e-20 endparam title="caleb-rsp" } evcarter-01(XAXIS) { ;replaces "carter" ;bailout setting added init: z=#pixel c=2 loop: z=(z*z)+(c-1)+#pixel bailout: |z|<@bailout default: title = "carter-01" param bailout caption="bailout" default=4.0 min=1e-20 endparam } evcarter-03(XAXIS) { init: z=0.94 a=0.945 b=-1.55 c=2 loop: z=(z*z+b^2)+(a^3+c-1)+#pixel bailout: |z|<@bailout default: title = "carter-03" center=(-5.2729,-0.04004) magn=0.699 param bailout caption="bailout" default=4.0 min=1e-20 endparam } emilie-01(XAXIX){ ;bailout setting added init: z=#pixel a=1 b=2 c=#pixel loop: z=a+z^3-b+c bailout: |z|<@bailout default: title = "emilie-01" param bailout caption="bailout" default=4.0 min=1e-20 endparam } kate-04 { ;this really belongs to Rui ;I used some of his ;tutorial, etc settings init: a=1 b=2 c = #pixel if @ca == 0 z=#pixel elseif @ca == 1 z = -2/(3*b) elseif @ca == 2 z= @cut endif loop: z=z*z*z+a+b^2+c*(z+2)+#pixel bailout: |z|<@bailout default: title = "kate-04" center=(-1.345,-0.01) magn=3.44828 param CA enum="pixel" "critical" "user" default=0 endparam param cut default = (0,0) caption = "Cut plane" endparam param bailout caption="bailout" default=4.0 min=1e-20 endparam } kate-01 { ;replaces "kate" ;the center and bailout ;have been reset init: z=0 loop: z=z*z*z+(z+2)+#pixel bailout: |z|<@bailout default: title = "kate-01" center=(-2.055,-0.045) magn=1 param bailout caption="bailout" default=4.0 min=1e-20 endparam } kate-02(XAXIS) { init: z = 0 loop: z = (z*z*z^2-pixel) + P2 bailout: |z| <= P2+3 default: title = "kate-02" param bailout caption="bailout" default=4.0 min=1e-20 endparam } michel-01 { init: z=#pixel a=1 b=2 c=#pixel loop: z=a+b+z^3+b*z+c bailout: |z|<4 default: title = "michel-01" } michel-02a{ init: z=#pixel a=1 b=2 c=#pixel loop: z=a+b+z^3-b*z+c bailout: |z|<@bailout default: title = "michel-02a" param bailout caption="bailout" default=4.0 min=1e-20 endparam } evmichel-04{ init: z=#pixel a=1 b=2 c=#pixel if @ca == 0 z=#pixel elseif @ca == 1 z = -2/(3*b) elseif @ca == 2 z= @cut endif loop: z=a+b+z^3-b*z+c bailout: |z|<@bailout default: title = "michel-04" param CA enum="pixel" "critical" "user" default=0 endparam param cut default = (0,0) caption = "Cut plane" endparam param bailout caption="bailout" default=4.0 min=1e-20 endparam } evwillar-01{ ;Use param settings ;to get interesting variations init: z=#pixel a=@ma b=@mb c=#pixel loop: z=a+b+z^3-b*z+c bailout: |z|<@bailout default: title = "willar-01" PARAM MA default=(1.0,0.0) caption="coeff A" Hint="A in a+b+z^3-bz+c" endparam param MB default=(1.0,0.0) caption="coeff B" hint="b in a+b+z^3 -bz+c" endparam param bailout caption="bailout" default=4.0 min=1e-20 endparam } evzacchi-01 { init: z=0 loop: z=z*z*z+(z+2)+#pixel bailout: |z|<@bailout default: title = "zacchi-01" center=(-2.0005,-0.0359) magn=0.781 angle=89.55 param bailout caption="bailout" default=4.0 min=1e-20 endparam } evzacchi-02(YAXIS) { init: z=0 a=2 b=1.0 loop: z=z*z*z+a*b*z+#pixel bailout: |z|<@bailout default: title = "zacchi-02" param bailout caption="bailout" default=4.0 min=1e-20 endparam } evwillar-02a { ;there are three faint ;circles. I don't know ;if this is a real fractal ;but if one applies some ;param changes and ;outside coloring ;something of interest can ;be achieved. init: a=1 b=1 c = #pixel if @ca == 0 z=#pixel elseif @ca == 1 z = -2/(2*b) elseif @ca == 2.0 z= @cut endif loop: z=(2+a)+b+z^3+(b*2+z+c) bailout: |z|<@bailout default: title = "willar-02a" center=(-0.33905,-0.4417424) magn=0.4867 param CA enum="pixel" "critical" "user" default=0 endparam param cut default = (1,0) caption = "Cut plane" endparam param bailout caption="bailout" default=4.0 min=1e-20 endparam } evemilie-02 { ;thank you Rui init: z=#pixel a=@a b=@b c=#pixel M=@fM N=@fN loop: z=a*b*z^3+a*z^2+c x=real(z) y=imag(z) bailout: ;bailout:|z|<@bailout X^2/M^2 + Y^2/N^2 <=1 default: title = "emilie-02" center=(-0.2,0.0) param a default=(1.0,0.0) caption= "param a" endparam param b default=(1.0,0.0) caption="param b" endparam param fM default=2.0 caption="ellipse xaxis width" Hint="the xaxis lenght for the elliptical trap" endparam param fN default=1.0 Caption="ellipse yaxis width" hint="the yaxis length for the elliptical trap" endparam } emilie(XAXIX){ init: z=#pixel a=1 b=2 c=#pixel loop: z=a+z^3-b+c bailout: |z|<4 default: title = "emilie" }