ConchoidofNicomedes2 { ;Caryn Paris-04-04-07-My first successful original formula ;A curve with the polar coordinates, ; r=b+a*sec(theta), ;and Cartesian coordinates, ; (x-a)2(x2+y2)=b^2x2 " ; ;The above information may be found here: ; http://mathworld.wolfram.com/ConchoidofNicomedes.htm ;A search also turns up many more sites. ; ;Try changing the bailout value. As it decreases, the image becomes smaller ;and less detailed. As it increases the image becomes larger and turns ;inward. ;As the multiplier changes, the image changes in size, shifts along the x-axis ;by roughly the negative of the multiplier, and deforms. At zero, the image ;is a circle. As the absolute value of the multiplier increases, the image ;decreases in size and turns into the familiar Mandelbrot bug. Negative values ;of the multiplier reverse the image along the x-axis. ; init: z = @start loop: z = #pixel + @a*(1/cos(z)) bailout: |z| <= @bailout default: title = "Conchoid of Nicomedes 2" center = (0,0) maxiter = 250 param start caption = "Starting point" default = (0,0) endparam float param bailout caption = "Bailout value" default = 4.0 min = 1.0 \$IFDEF VER40 exponential = true \$ENDIF endparam float param a caption = "Multiplier" default = 0.1 ;min = -20 ;As the absolute value of a increases, the image ;max = 20 ;gets smaller and shifts left or right by roughly endparam ;the factor of the multiplier. switch: type = "ConchoidofNicomedes2J" seed = #pixel bailout = bailout } ConchoidofNicomedes2J { ;Caryn Paris 04-04-07 ;Use the eyedropper to find different julia sets. ;Try changing the bailout value. As it decreases, the image becomes smaller ;and less detailed. As it increases the image becomes larger and turns ;inward. ;As the multiplier changes, the image changes in size, shifts along the x-axis ;by roughly the negative of the multiplier, and deforms. At zero, the image ;is a circle. As the absolute value of the multiplier increases, the image ;decreases in size and turns into the familiar Mandelbrot bug. Negative values ;of the multiplier reverse the image along the x-axis. ; init: z = @seed loop: z = #pixel + @a*(1/cos(z)) bailout: |z| <= @bailout default: title = "Conchoid of Nicomedes 2J" center = (0,0) maxiter = 250 param start caption = "Starting point" default = (0,0) endparam float param bailout caption = "Bailout value" default = 4.0 min = 1.0 \$IFDEF VER40 exponential = true \$ENDIF endparam float param a ;As the absolute value of a increases, the image caption = "Multiplier" ;gets smaller and shifts left or right by roughly default = 0.1 ;the negative magnitude of the multiplier. endparam param seed caption = "J seed" default = (-1.6, 0) endparam switch: type = "ConchoidofNicomedes2" bailout = bailout } DiffractionTheory2J { ; Formula loosely derived from definitions of Fresnel Integrals, used in diffraction theory init: z = @seed loop: z = sin((z+#pixel)^2) + cos((z+#pixel)^2) + @seed bailout: |z| < @bailout default: title = "Diffraction Theory 2J" param seed caption = "seed" ;default = (0,0) endparam param bailout default = 1 endparam switch: ;This switch essentially lets you pick the starting point for the 'M' type = "DiffractionTheory2M" ;formula in the same way as the @seed parameter in the corresponding bailout = bailout ;'M' formula does for the 'J' formula. start = #pixel } DiffractionTheory2alt { ; Formula loosely derived from definitions of Fresnel Integrals, used in diffraction theory init: z = @seed loop: z = sin((z+#pixel)^@power1) + cos((z+#pixel)^@power2) + @seed bailout: |z| < @bailout default: title = "Diffraction Theory 2Jalt" param seed caption = "seed" default = (0,0) endparam param bailout default = 0.977 min = 0.000001 endparam complex param power1 default = 2 endparam complex param power2 default = 2 endparam } DiffractionTheory2M { ; Formula loosely derived from definitions of Fresnel Integrals, used in diffraction theory init: z = @start loop: z = sin((z+#pixel)^2) + cos((z+#pixel)^2) + #pixel bailout: |z| < @bailout default: title = "Diffraction Theory 2M" param start caption = "start" default = (0,0) endparam param bailout default = 1 min = 0.000001 endparam switch: type = "DiffractionTheory2J" bailout = bailout @seed = #pixel } cascadingFractal { init: z = 0 loop: z = flip (z - #pixel)^(#pixel + #pixel) bailout: |z| < 4 default: title = "cascading fractal" } cascadingFractal2 { init: z = 0 loop: z = conj (z - #pixel)^(#pixel + #pixel) bailout: |z| < 4 default: title = "cascading fractal2" } cascadingFractal3 { init: z = 0 loop: z = flip (z - #pixel)^(-(#pixel + #pixel)) bailout: |z| < 4 default: title = "cascading fractal3" } cascadingFractal4 { init: z = 0 loop: z = conj (z - #pixel)^(-(#pixel + #pixel)) bailout: |z| < 4 default: title = "cascading fractal4" }