Click on an image to go directly to a system or scroll to see all of the systems in this gallery.

 OdeFactory Images and Annotations An OdeFactory Slide Show Click on a slide to zoom in. Click "video" to see a video. View/Sys/Gal: Ode " Intro to InfiniteImages" in "InfiniteImages."Range: (vMax,vMin) = (5.000,-5.000), (hMin,hMax) = (-5.000,5.000)VFld: (0)This gallery consists of a collection of images all of which are generated from time-scaled versions of the two closely related vector fields which define system "(28b EMap)" in gallery HopalongEMaps:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%dand system "EMap 13.3" in gallery ArtGallery:        x <- y-sgn(x)*sqrt(abs(b%x-c)),        y <- a-x*d.The only difference between the two systems is the interchange of operators * and % in terms b*x-c and x%d. The %* examples begin at system (10b EMap) in this gallery.Both systems are variations of the classic Barry Martin "Hopalong" system:        x <- y-sgn(x)*sqrt(abs(b*x-c))),        y <- a-x.For details, see "Computers in Art, Design and Animation," Springer-Verlag, 1989.Parameter s is used to time-scale the system. By increasing s you can decrease the amount of black in an image.In theory, it is possible to generate millions of different EMap images from a single vector field. For example, in this case, the system has 5 parameters, each of which may have 10 or more interesting values. There are 11 color tables that can be used. Finally, suppose the system has 10 different interesting viewing regions. This gives on the order of 10^7, or 10 million, combinations of parameter values, color tables and viewing regions to explore.In practice, most of the 10 million images would not be recognizably different to the human eye. It may be more reasonable to assume that about 3 values of each parameter, 3 color tables and 5 viewing regions are of interest. This gives 3^6*5 = 3645 discernible interesting images.The 108 images associated with the 99 systems in this gallery took a few days to create: by varying parameters, color tables and viewing regions. To generate 3645 images would take about 60 days. An "art critic" algorithm would be needed to sift through the large number of possible images to select the most artistic images. View/Sys/Gal: EMap "( 0) EMapCT0" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0 View/Sys/Gal: EMap "( 0) EMapCT1" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 1 View/Sys/Gal: EMap "( 0) EMapCT10" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 10 View/Sys/Gal: EMap "( 0) EMapCT2" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 2 View/Sys/Gal: EMap "( 0) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 3 View/Sys/Gal: EMap "( 0) EMapCT4" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 4 View/Sys/Gal: EMap "( 0) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 5 View/Sys/Gal: EMap "( 0) EMapCT6" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 6 View/Sys/Gal: EMap "( 0) EMapCT7" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 7 View/Sys/Gal: EMap "( 0) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 8 View/Sys/Gal: EMap "( 0) EMapCT9" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 9 View/Sys/Gal: EMap "( 1) EMap view 1" in "InfiniteImages."Range: (vMax,vMin) = (19.302,-12.607), (hMin,hMax) = (-10.000,50.000)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0This is "( 0) EMap" again with a different viewing area. Note the change in the vMax, vMin, hMin and hMax values. View/Sys/Gal: EMap "( 1) EMap view 2" in "InfiniteImages."Range: (vMax,vMin) = (16.588,12.657), (hMin,hMax) = (596.558,599.966)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0Just a different part of "( 0) EMap view 0." View/Sys/Gal: EMap "( 1) EMap view 3" in "InfiniteImages."Range: (vMax,vMin) = (14.384,13.050), (hMin,hMax) = (598.868,599.929)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0A part of "( 1) EMap view 2." View/Sys/Gal: EMap "( 1) EMap view 4" in "InfiniteImages."Range: (vMax,vMin) = (13.576,12.540), (hMin,hMax) = (600.734,601.488)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0 View/Sys/Gal: EMap "( 1) EMapCT3 view 5" in "InfiniteImages."Range: (vMax,vMin) = (14.384,13.050), (hMin,hMax) = (598.868,599.929)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 3A different CT applied to "( 1) EMap view 3." View/Sys/Gal: EMap "( 2) EMap" in "InfiniteImages."Range: (vMax,vMin) = (13.311,9.323), (hMin,hMax) = (597.615,601.386)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s = .88; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s = .88;EMap CT: 0Images for systems "( 2) EMap ..." through "( 9) EMap ..." are generated by varying parameters a, b, c, d and s, color tables CT0 ... CT10 and view parameters vMax, vMin, hMin and hMax. View/Sys/Gal: EMap "( 2b) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (15.932,7.956), (hMin,hMax) = (595.704,603.246)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.350; d = 5.500; s = 3.400; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.350;         d = 5.500; s = 3.400; EMap CT: 3 View/Sys/Gal: EMap "( 2c) EMapCT7" in "InfiniteImages."Range: (vMax,vMin) = (13.960,9.126), (hMin,hMax) = (599.888,604.078)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.350; d = 5.500; s = 3.400; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.350;         d = 5.500; s = 3.400; EMap CT: 7 View/Sys/Gal: EMap "( 2d) EMapCT6" in "InfiniteImages."Range: (vMax,vMin) = (14.755,11.919), (hMin,hMax) = (598.267,600.725)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.350; d = 5.500; s = 3.400; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.350;         d = 5.500; s = 3.400; EMap CT: 6 View/Sys/Gal: EMap "( 3) EMap" in "InfiniteImages."Range: (vMax,vMin) = (14.480,11.338), (hMin,hMax) = (598.704,601.155)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.36; d = 5.60; s = .46; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.36;         d = 5.60; s = .46; EMap CT: 0 View/Sys/Gal: EMap "( 3b) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (14.480,11.338), (hMin,hMax) = (598.704,601.155)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.36; d = 5.60; s = .46; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.36;         d = 5.60; s = .46; EMap CT: 3 View/Sys/Gal: EMap "( 3c) EMapCT9" in "InfiniteImages."Range: (vMax,vMin) = (13.905,12.496), (hMin,hMax) = (599.438,600.445)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.36; d = 5.60; s = .46; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.36;         d = 5.60; s = .46; EMap CT: 9 View/Sys/Gal: EMap "( 4) EMap" in "InfiniteImages."Range: (vMax,vMin) = (12.125,10.278), (hMin,hMax) = (594.180,595.369)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.30; b = -.18; c = -.41;         d = 5.10; s = 2.90; EMap CT: 0 View/Sys/Gal: EMap "( 4b) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (12.217,10.371), (hMin,hMax) = (594.121,595.309)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.30; b = -.18; c = -.41;         d = 5.10; s = 2.90; EMap CT: 3 View/Sys/Gal: EMap "( 4c) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (10.796,10.082), (hMin,hMax) = (596.234,596.620)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.300; b = -.180; c = -.410; d = 5.200; s = 1.600; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.300; b = -.180; c = -.410;         d = 5.200; s = 1.600; EMap CT: 3 View/Sys/Gal: EMap "( 4d) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (4.948,3.098), (hMin,hMax) = (40.800,42.800)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.30; b = -.18; c = -.41;         d = 5.10; s = 2.90; EMap CT: 3 View/Sys/Gal: EMap "( 5) EMap" in "InfiniteImages."Range: (vMax,vMin) = (6.970,3.825), (hMin,hMax) = (1.589,3.412)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.60; b = -.17; c = -.22; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.60; b = -.17; c = -.22;         d = 5.10; s = 2.90; EMap CT: 0 View/Sys/Gal: EMap "( 5b) EMapCT10" in "InfiniteImages."Range: (vMax,vMin) = (6.970,3.825), (hMin,hMax) = (1.589,3.412)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.60; b = -.17; c = -.22; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.60; b = -.17; c = -.22;         d = 5.10; s = 2.90; EMap CT: 10 View/Sys/Gal: EMap "( 5c) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (5.992,5.217), (hMin,hMax) = (2.306,2.717)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.600; b = -.170; c = -.180; d = 5.100; s = 5.100; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.600; b = -.170; c = -.180;         d = 5.100; s = 5.100; EMap CT: 5 View/Sys/Gal: EMap "( 6) EMap" in "InfiniteImages."Range: (vMax,vMin) = (6.970,3.825), (hMin,hMax) = (1.589,3.412)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.60; b = -.17; c = -.40; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.60; b = -.17; c = -.40;         d = 5.10; s = 2.90; EMap CT: 0 View/Sys/Gal: EMap "( 6b) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (6.655,3.510), (hMin,hMax) = (1.589,3.412)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.170; c = -.400; d = 5.100; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.170; c = -.400;         d = 5.100; s = 2.900; EMap CT: 3 View/Sys/Gal: EMap "( 6c) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (6.655,3.510), (hMin,hMax) = (1.589,3.412)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.150; c = -.400; d = 5.100; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.150; c = -.400;         d = 5.100; s = 2.900; EMap CT: 3 View/Sys/Gal: EMap "( 6d) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (8.306,-2.673), (hMin,hMax) = (-0.119,5.715)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.150; c = -.400; d = 2.800; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.150; c = -.400;         d = 2.800; s = 2.900; EMap CT: 5 View/Sys/Gal: EMap "( 6e) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (3.939,0.012), (hMin,hMax) = (3.540,5.293)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.150; c = -.400; d = 2.800; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.150; c = -.400;         d = 2.800; s = 2.900; EMap CT: 3 View/Sys/Gal: EMap "( 6f) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (6.589,-0.171), (hMin,hMax) = (1.563,4.330)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.150; c = -.280; d = 5.000; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.150; c = -.280;         d = 5.000; s = 2.900; EMap CT: 3 View/Sys/Gal: EMap "( 6g) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (4.544,2.374), (hMin,hMax) = (2.556,3.936)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.600; b = -.120; c = -.280; d = 5.300; s = 3.500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.600; b = -.120; c = -.280;         d = 5.300; s = 3.500; EMap CT: 8 View/Sys/Gal: EMap "( 6h) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (4.544,2.374), (hMin,hMax) = (2.556,3.936)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.600; b = -.120; c = -.280; d = 5.300; s = 3.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.600; b = -.120; c = -.280;         d = 5.300; s = 3.900; EMap CT: 3 View/Sys/Gal: EMap "( 7) EMap" in "InfiniteImages."Range: (vMax,vMin) = (16.159,14.951), (hMin,hMax) = (598.015,598.974)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: EMap "( 7b) EMap" in "InfiniteImages."Range: (vMax,vMin) = (16.166,14.339), (hMin,hMax) = (597.848,599.179)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.500; b = -.140; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.500; b = -.140; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: EMap "( 7c) EMap" in "InfiniteImages."Range: (vMax,vMin) = (16.713,13.061), (hMin,hMax) = (597.183,599.844)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.500; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.500; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: EMap "( 7d) EMap" in "InfiniteImages."Range: (vMax,vMin) = (14.573,13.363), (hMin,hMax) = (598.903,599.711)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.500; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.500; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: EMap "( 7e) EMap" in "InfiniteImages."Range: (vMax,vMin) = (13.701,13.139), (hMin,hMax) = (599.328,599.673)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.500; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.500; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: EMap "( 7f) EMapCT4" in "InfiniteImages."Range: (vMax,vMin) = (13.504,12.941), (hMin,hMax) = (599.328,599.672)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.400; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.400; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 4 View/Sys/Gal: EMap "( 7g) EMapCT4" in "InfiniteImages."Range: (vMax,vMin) = (13.363,12.801), (hMin,hMax) = (599.328,599.672)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.400; b = -.150; c = -.300; d = 5.500; s = .300; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.400; b = -.150; c = -.300;         d = 5.500; s = .300; EMap CT: 4 View/Sys/Gal: EMap "( 7h) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (13.693,13.209), (hMin,hMax) = (598.952,599.248)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.500; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.500; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 8 View/Sys/Gal: EMap "( 7i) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (13.887,13.403), (hMin,hMax) = (599.041,599.337)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.600; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.600; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 8 View/Sys/Gal: EMap "( 7j) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (14.613,12.677), (hMin,hMax) = (598.596,599.781)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.600; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.600; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 8 View/Sys/Gal: EMap "( 7k) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (17.517,9.772), (hMin,hMax) = (596.819,601.559)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.600; b = -.150; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.600; b = -.150; c = -.300;         d = 5.500; s = .120; EMap CT: 8 View/Sys/Gal: EMap "( 7l) EMapCT9" in "InfiniteImages."Range: (vMax,vMin) = (11.325,10.762), (hMin,hMax) = (599.506,599.822)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.600; b = -.150; c = -.300; d = 5.500; s = .210; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.600; b = -.150; c = -.300;         d = 5.500; s = .210; EMap CT: 9 View/Sys/Gal: EMap "( 7m) EMapCT8" in "InfiniteImages."Range: (vMax,vMin) = (11.325,10.762), (hMin,hMax) = (599.506,599.822)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.600; b = -.150; c = -.300; d = 5.500; s = .210; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.600; b = -.150; c = -.300;         d = 5.500; s = .210; EMap CT: 8 View/Sys/Gal: EMap "( 7n) EMapCT0" in "InfiniteImages."Range: (vMax,vMin) = (1.236,0.217), (hMin,hMax) = (3.021,3.877)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.300; d = 5.500; s = .420; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.300;         d = 5.500; s = .420; EMap CT: 0 View/Sys/Gal: EMap "( 8) EMap" in "InfiniteImages."Range: (vMax,vMin) = (6.569,-1.309), (hMin,hMax) = (-1.281,5.941)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: IMap "( 8) IMap0011" in "InfiniteImages."Range: (vMax,vMin) = (6.569,-1.309), (hMin,hMax) = (-1.281,5.941)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.140; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.140; c = -.300;         d = 5.500; s = .120;Vary the parameters. View/Sys/Gal: EMap "( 8b) EMap" in "InfiniteImages."Range: (vMax,vMin) = (6.569,-1.309), (hMin,hMax) = (-1.281,5.941)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.050; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.050; c = -.300;         d = 5.500; s = .120; EMap CT: 0 View/Sys/Gal: IMap "( 8b) IMap0011" in "InfiniteImages."Range: (vMax,vMin) = (6.569,-1.309), (hMin,hMax) = (-1.281,5.941)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.050; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.050; c = -.300;         d = 5.500; s = .120;Vary the parameters.Also see the EMap view. View/Sys/Gal: IMap "( 8c) IMap0011" in "InfiniteImages."Range: (vMax,vMin) = (6.259,-1.619), (hMin,hMax) = (-1.701,5.521)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.300; b = -.029; c = -.060; d = 5.000; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.300; b = -.029; c = -.060;         d = 5.000; s = .120;Vary the parameters. View/Sys/Gal: EMap "( 9) EMapCT1" in "InfiniteImages."Range: (vMax,vMin) = (22.382,11.933), (hMin,hMax) = (600.270,608.990)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = -.800; b = .490; c = -.250; d = 8.700; s = 4.600; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = -.800; b = .490; c = -.250;         d = 8.700; s = 4.600; EMap CT: 1Try the various color tables.Investigate the IMap. View/Sys/Gal: EMap "( 9b) EMapCT6" in "InfiniteImages."Range: (vMax,vMin) = (17.484,15.204), (hMin,hMax) = (600.291,602.035)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = -.800; b = .490; c = -.250; d = 8.700; s = 4.600; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = -.800; b = .490; c = -.250;         d = 8.700; s = 4.600; EMap CT: 6 View/Sys/Gal: EMap "( 9c) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (17.717,15.437), (hMin,hMax) = (600.301,602.045)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = -.800; b = .490; c = -.120; d = 8.700; s = 4.600; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = -.800; b = .490; c = -.120;         d = 8.700; s = 4.600; EMap CT: 3 View/Sys/Gal: EMap "( 9d) EMapCT6" in "InfiniteImages."Range: (vMax,vMin) = (17.991,17.273), (hMin,hMax) = (600.327,600.831)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = -.720; b = .540; c = -.120; d = 8.700; s = 10.000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = -.720; b = .540; c = -.120;         d = 8.700; s = 10.000; EMap CT: 6 View/Sys/Gal: Ode "(10a) EMap" in "InfiniteImages."Range: (vMax,vMin) = (27.277,-4.627), (hMin,hMax) = (584.424,614.592)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.35; d = 5.50; s=0This is a zoomed out view of the system that was used to generate the first 60+ images named, ( 0) through ( 9), by varying parameters, color tables and viewing areas.Notice that the EMap view has repeated segments that are similar, but not exactly the same, that extend forever in the x direction. The % operator used in the computation of the new y part is causing the repetition when the new y values are used to compute the new x values. The y values oscillate but are bounded.The iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.35;         d = 5.50; s=0EMap CT: 0Image 1: EMap view.Image 2: colored vector field in the Ode view. View/Sys/Gal: Ode "(10b) EMap" in "InfiniteImages."Range: (vMax,vMin) = (10.000,-10.000), (hMin,hMax) = (-10.000,10.000)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.44; b = -4.70; c = 9.40; d = 1.10; s=0This is a different kind of variation of the first system. Two operators in the first system have been swapped in two terms of the defining vector field. The multiplication operator (*) and the mod (%) operator have been swapped in the         b*x-c and x%dterms.Neither x or y is bounded and there is no longer any global repetition of the basic pattern. The image is localized about the origin. The basic symmetry of the system is about the diagonal line y = -x. If you look closely, you will notice that the symmetry is not exact.The interesting structure of this system is difficult to see at this scale. The trick to generating a lot of interesting images from the system is to choose a color table that gives a very fragmented image, say CT5, and then zoom in and select and modify small regions of the image using different parameter values and color tables.The iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.44; b = -4.70; c = 9.40;         d = 1.10; s=0EMap CT: 0Image 1: EMap view.Image 2: colored vector field in the Ode view. View/Sys/Gal: EMap "(11) EMap" in "InfiniteImages."Range: (vMax,vMin) = (-2.053,-2.067), (hMin,hMax) = (-1.806,-1.795)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.44; b = -4.70; c = 9.40; d = 1.10; s=0The rest of the images, named "(11) ..." are variations of second version of the first system where % and * were swapped.They are not simply variations of the first 60+ images in that they use completely different values of the parameters, the color tables and the viewing areas.The iteration is now defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.44; b = -4.70; c = 9.40;         d = 1.10;EMap CT: 0Can you find the first image in the system "(10b) EMap" image?Hint: zoom out on image "(10b) EMap."The 11 images for this system differ only in the color tables being used.Examples named "(12) ..." primarily involve variations of the parameters and viewing regions for the system. View/Sys/Gal: EMap "(11b) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (-2.053,-2.067), (hMin,hMax) = (-1.806,-1.795)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.460; b = -4.700; c = 9.400; d = 1.100; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.460; b = -4.700;         c = 9.400; d = 1.100; s = .000; EMap CT: 5 View/Sys/Gal: EMap "(11c) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (-1.927,-2.067), (hMin,hMax) = (-1.859,-1.742)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.460; b = -4.700; c = 9.400; d = 1.100; s = .000; Image (11b) zoomed out and shifted down.This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.460; b = -4.700; c = 9.400;         d = 1.100; s = .000; EMap CT: 5 View/Sys/Gal: EMap "(11d) EMapCT1" in "InfiniteImages."Range: (vMax,vMin) = (-1.988,-2.014), (hMin,hMax) = (-1.833,-1.813)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.460; b = -4.700; c = 9.400; d = 1.100; s = .000; Part of (11c).This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.460; b = -4.700; c = 9.400;         d = 1.100; s = .000; EMap CT: 1 View/Sys/Gal: EMap "(11e) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (-5.315,-5.921), (hMin,hMax) = (-1.272,-0.845)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.480; b = -4.700; c = 9.400; d = 1.100; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.480; b = -4.700; c = 9.400;         d = 1.100; s = .000; EMap CT: 3Image 1: CT3Image 2: CT6 View/Sys/Gal: EMap "(11f) EMapCT9" in "InfiniteImages."Range: (vMax,vMin) = (9.785,-9.628), (hMin,hMax) = (-6.890,6.788)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = .440; b = 7.100; c = -6.000; d = 1.900; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = .440; b = 7.100; c = -6.000;         d = 1.900; s = .000; EMap CT: 9 View/Sys/Gal: EMap "(11g) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (11.138,-11.138), (hMin,hMax) = (-7.143,7.244)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = .580; b = -2.600; c = 8.500; d = -1.500; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = .580; b = -2.600; c = 8.500;         d = -1.500; s = .000; EMap CT: 5Image 1: CT5Image 2: CT2 View/Sys/Gal: EMap "(12) EMap" in "InfiniteImages."Range: (vMax,vMin) = (5.325,4.955), (hMin,hMax) = (1.172,1.484)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.270; b = -4.700; c = 9.400; d = 1.100; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.270; b = -4.700; c = 9.400;         d = 1.100; s = .000; EMap CT: 0 View/Sys/Gal: EMap "(12b) EMap" in "InfiniteImages."Range: (vMax,vMin) = (5.201,5.127), (hMin,hMax) = (1.269,1.332)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.270; b = -4.700; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.270; b = -4.700; c = 9.400;         d = 1.100; s = .500; EMap CT: 0Image 1: CT0Image 2: CT3Image 3: CT8 View/Sys/Gal: EMap "(12c) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (5.038,4.805), (hMin,hMax) = (1.290,1.470)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.270; b = -4.700; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.270; b = -4.700; c = 9.400;         d = 1.100; s = .500; EMap CT: 3 View/Sys/Gal: EMap "(12d) EMapCT2" in "InfiniteImages."Range: (vMax,vMin) = (5.026,4.793), (hMin,hMax) = (1.290,1.470)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.700; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.700; c = 9.400;         d = 1.100; s = .500; EMap CT: 2 View/Sys/Gal: EMap "(12e) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (4.999,4.943), (hMin,hMax) = (1.359,1.398)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .500; EMap CT: 5 View/Sys/Gal: EMap "(12f) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (4.987,4.931), (hMin,hMax) = (1.376,1.415)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .500; EMap CT: 5 View/Sys/Gal: EMap "(12g) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (4.971,4.916), (hMin,hMax) = (1.392,1.431)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .510; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .510; EMap CT: 5 View/Sys/Gal: EMap "(12h) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (5.050,4.980), (hMin,hMax) = (1.281,1.326)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .500; EMap CT: 5 View/Sys/Gal: EMap "(12i) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (5.038,5.032), (hMin,hMax) = (1.305,1.308)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .500; EMap CT: 5Image 1: CT5Image 2: CT8Image 3: CT2Image 4: CT1 View/Sys/Gal: EMap "(12j) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (5.184,5.173), (hMin,hMax) = (1.329,1.334)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.160; b = -4.600; c = 9.400; d = 1.100; s = .500; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.160; b = -4.600; c = 9.400;         d = 1.100; s = .500; EMap CT: 5 View/Sys/Gal: EMap "new ( 0) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (13.319,9.331), (hMin,hMax) = (597.622,601.393)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.9000; b = -.1400; c = -.3500; d = 5.5000; s = 1.0000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.9000; b = -.1400; c = -.3500;         d = 5.5000; s = 1.0000; EMap CT: 3 View/Sys/Gal: EMap "new ( 0) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (11.892,10.487), (hMin,hMax) = (604.076,605.266)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.9000; b = -.1400; c = .8000; d = 4.6000; s = 5.9000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.9000; b = -.1400; c = .8000;         d = 4.6000; s = 5.9000; EMap CT: 5 View/Sys/Gal: EMap "new ( 1) EMapCT1 view 2" in "InfiniteImages."Range: (vMax,vMin) = (16.610,12.300), (hMin,hMax) = (597.900,602.100)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.9000; b = -.1500; c = -.3500; d = 5.0000; s = .0000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.9000; b = -.1500; c = -.3500;         d = 5.0000; s = .0000; EMap CT: 1This is a single image, not a tiled image. View/Sys/Gal: EMap "new ( 1) EMapCT3 view 1" in "InfiniteImages."Range: (vMax,vMin) = (-2.682,-5.892), (hMin,hMax) = (22.434,28.034)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.9000; b = -.1400; c = .2200; d = 5.5000; s = .0100; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.9000; b = -.1400; c = .2200;         d = 5.5000; s = .0100; EMap CT: 3 View/Sys/Gal: EMap "new ( 3) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (16.367,10.867), (hMin,hMax) = (597.175,601.235)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.90; b = -.14; c = -.36; d = 5.60; s = .46; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.90; b = -.14; c = -.36;         d = 5.60; s = .46; EMap CT: 5 View/Sys/Gal: EMap "new ( 4) EMapCT2" in "InfiniteImages."Range: (vMax,vMin) = (5.433,0.142), (hMin,hMax) = (0.362,5.100)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.3000; b = -.1800; c = -.4100; d = 5.1000; s = 8.9000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.3000; b = -.1800; c = -.4100;         d = 5.1000; s = 8.9000; EMap CT: 2 View/Sys/Gal: EMap "new ( 4d) EMapCT5" in "InfiniteImages."Range: (vMax,vMin) = (4.750,4.202), (hMin,hMax) = (41.595,42.258)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.30; b = -.18; c = -.41;         d = 5.10; s = 2.90; EMap CT: 5 View/Sys/Gal: EMap "new ( 5) EMapCT9" in "InfiniteImages."Range: (vMax,vMin) = (8.080,-1.984), (hMin,hMax) = (-0.228,5.606)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.6000; b = -.1700; c = -.2200; d = 5.1000; s = 5.0000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.6000; b = -.1700; c = -.2200;         d = 5.1000; s = 5.0000; EMap CT: 9 View/Sys/Gal: EMap "new ( 6) EMapCT1" in "InfiniteImages."Range: (vMax,vMin) = (7.060,3.430), (hMin,hMax) = (0.790,4.160)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.6000; b = -.1600; c = -.4000; d = 5.3000; s = 2.9000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.6000; b = -.1600; c = -.4000;         d = 5.3000; s = 2.9000; Image 1: EMap CT: 1.Image 2: EMap CT: 8. View/Sys/Gal: EMap "new ( 6c) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (6.314,5.014), (hMin,hMax) = (2.464,3.135)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.100; b = -.150; c = -.400; d = 5.100; s = 2.900; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.100; b = -.150; c = -.400;         d = 5.100; s = 2.900; EMap CT: 3 View/Sys/Gal: EMap "new ( 6f) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (6.418,5.037), (hMin,hMax) = (2.373,3.173)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 6.1000; b = -.1500; c = -.2800; d = 5.0000; s = 3.2000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 6.1000; b = -.1500; c = -.2800;         d = 5.0000; s = 3.2000; EMap CT: 3 View/Sys/Gal: EMap "new ( 7) EMapCT7" in "InfiniteImages."Range: (vMax,vMin) = (16.665,11.468), (hMin,hMax) = (595.253,599.161)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 5.0000; b = -.1400; c = -.3000; d = 5.0000; s = 1.1000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 5.0000; b = -.1400; c = -.3000;         d = 5.0000; s = 1.1000; EMap CT: 7 View/Sys/Gal: EMap "new ( 7d) EMap" in "InfiniteImages."Range: (vMax,vMin) = (14.652,13.442), (hMin,hMax) = (598.624,599.432)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.5000; b = -.1600; c = -.3000; d = 5.5000; s = 1.0000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.5000; b = -.1600; c = -.3000;         d = 5.5000; s = 1.0000; EMap CT: 0 View/Sys/Gal: EMap "new ( 7h) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (14.649,13.243), (hMin,hMax) = (598.724,599.499)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.5000; b = -.1500; c = -.3000; d = 5.5000; s = .5100; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.5000; b = -.1500; c = -.3000;         d = 5.5000; s = .5100; EMap CT: 3 View/Sys/Gal: EMap "new ( 8) EMapCT3" in "InfiniteImages."Range: (vMax,vMin) = (0.480,-4.940), (hMin,hMax) = (-0.990,1.960)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = -4.8000; b = -.1200; c = -.3100; d = 5.6000; s = 1.0000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = -4.8000; b = -.1200; c = -.3100;         d = 5.6000; s = 1.0000; EMap CT: 3 View/Sys/Gal: EMap "new ( 8b) EMapCT6" in "InfiniteImages."Range: (vMax,vMin) = (4.920,3.500), (hMin,hMax) = (3.936,5.198)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 4.900; b = -.050; c = -.300; d = 5.500; s = .120; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 4.900; b = -.050; c = -.300;         d = 5.500; s = .120; EMap CT: 6 View/Sys/Gal: EMap "new ( 8b) EMapMaxCT5" in "InfiniteImages."Range: (vMax,vMin) = (2.396,2.313), (hMin,hMax) = (1.665,1.729)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x%d)), a = 3.9000; b = -.0360; c = -.6500; d = 7.5000; s = 6.9000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x%d).Parameters are:         a = 3.9000; b = -.0360; c = -.6500;         d = 7.5000; s = 6.9000; EMap CT: 5 View/Sys/Gal: EMap "new (11c) EMapMaxCT5" in "InfiniteImages."Range: (vMax,vMin) = (-0.200,-2.587), (hMin,hMax) = (-2.050,-1.610)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),(1+s*.01)*(a-x*d)), a = -.460; b = -4.700; c = 9.400; d = 1.100; s = .000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b%x-c))),        y <- (1+s*.01)*(a-x*d).Parameters are:         a = -.460; b = -4.700; c = 9.400;         d = 1.100; s = .000; EMap CT: 5