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 " Introduction" in "HopalongEMaps."Range: (vMax,vMin) = (5.000,-5.000), (hMin,hMax) = (-5.000,5.000)VFld: (0)                IntroductionThe first group of systems in this gallery use the 2D hopalong iteration map defined by Barry Martin:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.The hopalong system was originally of interest as a 2D iteration map but it is also of visual interest when viewed using the escape-time display algorithm, called the "EMap" view in OdeFactory. The escape-time algorithm is most often used to display 2D fractals.You can change the parameters in the EMap, or IMap views, if you want to create your own variations of the graphic images.The next group of "10b" systems are time-scaled versions of the hopalong map.Another group of systems use a variation of the hopalong map where the y iteration has been changed to:        y <- a-x%d.The "%" is the Java remainder or modulus operator which applies to floats as well as to ints. For details regarding "%", see: Java mod operator.The final group of "28b" systems are time-scaled versions of the "%" variation of the hopalong map.Eleven color tables, CT0 through CT10, are available for the EMap images. In the EMap view, click in the graphics area to open a color table chooser. Note how the EMap images change using different color tables. View/Sys/Gal: EMap "( 1 EMap) a = -1.70; b = 9.50; c = 24.00;" in "HopalongEMaps."Range: (vMax,vMin) = (8.084,-11.916), (hMin,hMax) = (-10.360,9.640)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = -1.70; b = 9.50; c = 24.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = -1.70; b = 9.50; c = 24.00; View/Sys/Gal: IMap "( 1 IMap0011) a = -1.70; b = 9.50; c = 24.00;" in "HopalongEMaps."Range: (vMax,vMin) = (78.080,-81.920), (hMin,hMax) = (-80.360,79.640)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = -1.70; b = 9.50; c = 24.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = -1.70; b = 9.50; c = 24.00;Try selecting/deselecting "Show 2D IMap Orbit Sequence" on the Help menu. Notice the difference.Try selecting/deselecting "Hide Axes" on the Help menu. Notice the difference.Try selecting/deselecting "Hide Arrowheads/Seeds" on the Help menu. Notice the difference. View/Sys/Gal: EMap "( 2 EMap) a = .00; b = -.93; c = 5.00;" in "HopalongEMaps."Range: (vMax,vMin) = (9.960,-10.040), (hMin,hMax) = (-10.038,9.962)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .00; b = -.93; c = 5.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .00; b = -.93; c = 5.00; View/Sys/Gal: IMap "( 2 IMap0011) a = .00; b = -.93; c = 5.00;" in "HopalongEMaps."Range: (vMax,vMin) = (19.960,-20.040), (hMin,hMax) = (-20.040,19.960)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .00; b = -.93; c = 5.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .00; b = -.93; c = 5.00; View/Sys/Gal: EMap "( 3 EMap) a = .00; b = 1.00; c = 5.00;" in "HopalongEMaps."Range: (vMax,vMin) = (9.960,-10.040), (hMin,hMax) = (-10.038,9.962)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .00; b = 1.00; c = 5.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .00; b = 1.00; c = 5.00; View/Sys/Gal: IMap "( 3 IMap0011) a = .00; b = 1.00; c = 5.00;" in "HopalongEMaps."Range: (vMax,vMin) = (39.960,-40.040), (hMin,hMax) = (-40.040,39.960)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .00; b = 1.00; c = 5.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .00; b = 1.00; c = 5.00; View/Sys/Gal: EMap "( 4 EMap) a = 1.00; b = 1.00; c = 10.00;" in "HopalongEMaps."Range: (vMax,vMin) = (11.960,-8.040), (hMin,hMax) = (-10.040,9.960)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 1.00; b = 1.00; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 1.00; b = 1.00; c = 10.00; View/Sys/Gal: IMap "( 4 IMap0011) a = 1.00; b = 1.00; c = 10.00;" in "HopalongEMaps."Range: (vMax,vMin) = (11.960,-8.040), (hMin,hMax) = (-10.040,9.960)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 1.00; b = 1.00; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 1.00; b = 1.00; c = 10.00; View/Sys/Gal: EMap "( 5 EMap) a = 2.00; b = 2.10; c = 10.00;" in "HopalongEMaps."Range: (vMax,vMin) = (9.821,-5.129), (hMin,hMax) = (-7.094,7.094)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 2.00; b = 2.10; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 2.00; b = 2.10; c = 10.00; View/Sys/Gal: IMap "( 5 IMap0011) a = 2.00; b = 2.10; c = 10.00;" in "HopalongEMaps."Range: (vMax,vMin) = (17.300,-12.600), (hMin,hMax) = (-14.189,14.189)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 2.00; b = 2.10; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 2.00; b = 2.10; c = 10.00; View/Sys/Gal: EMap "( 6 EMap) a = 3.70; b = .98; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (7.470,-2.530), (hMin,hMax) = (-3.400,6.600)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.70; b = .98; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.70; b = .98; c = 1.30; View/Sys/Gal: IMap "( 6 IMap0011) a = 3.70; b = .98; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (2.662,1.412), (hMin,hMax) = (0.958,2.208)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.70; b = .98; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.70; b = .98; c = 1.30; View/Sys/Gal: EMap "( 7 EMap) a = 3.80; b = -5.20; c = 1.20;" in "HopalongEMaps."Range: (vMax,vMin) = (10.000,-5.000), (hMin,hMax) = (-5.000,9.000)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.80; b = -5.20; c = 1.20; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.80; b = -5.20; c = 1.20; View/Sys/Gal: IMap "( 7 IMap0011) a = 3.80; b = -5.20; c = 1.20;" in "HopalongEMaps."Range: (vMax,vMin) = (62.500,-57.500), (hMin,hMax) = (-54.000,58.000)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.80; b = -5.20; c = 1.20; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.80; b = -5.20; c = 1.20; View/Sys/Gal: EMap "( 8 EMap) a = 4.20; b = .70; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (7.794,-2.206), (hMin,hMax) = (-3.428,6.572)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.20; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.20; b = .70; c = 1.30;Try CT3. View/Sys/Gal: IMap "( 8 IMap0011) a = 4.20; b = .70; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (22.790,-17.210), (hMin,hMax) = (-18.430,21.570)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.20; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.20; b = .70; c = 1.30; View/Sys/Gal: EMap "( 9 EMap) a = 5.70; b = .70; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (8.154,-1.846), (hMin,hMax) = (-2.589,7.411)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 5.70; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 5.70; b = .70; c = 1.30; View/Sys/Gal: IMap "( 9 IMap0011) a = 5.70; b = .70; c = 1.30;" in "HopalongEMaps."Range: (vMax,vMin) = (13.150,-6.850), (hMin,hMax) = (-7.590,12.410)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 5.70; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 5.70; b = .70; c = 1.30; View/Sys/Gal: EMap "(10 EMap) a = 3.5; b=.125; c=0" in "HopalongEMaps."Range: (vMax,vMin) = (7.294,-2.706), (hMin,hMax) = (-3.428,6.572)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.80; b = .58; c = 1.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.80; b = .58; c = 1.00; View/Sys/Gal: System "(10 IMap0011) a = 3.80; b = .58; c = 1.00; ," in gallery "HopalongEMaps," renamed as "(10 IMap0011) a = 3.80; b = .58; c = 1.00;."Range: (vMax,vMin) = (22.290,-17.710), (hMin,hMax) = (-18.430,21.570)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.80; b = .58; c = 1.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.80; b = .58; c = 1.00; View/Sys/Gal: EMap "(10b EMap)" in "HopalongEMaps."Range: (vMax,vMin) = (7.294,-2.706), (hMin,hMax) = (-3.428,6.572)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.80; b = .58; c = 1.00; s=0This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.80; b = .58; c = 1.00; s=0This is a time-scaled version of (10).Increasing s brightens the EMap, i.e. decreases the amount of black in the image.Black regions, called basins of attraction, correspond to points that don't get farther than sqrt(50) from (0,0) after 100 iterations, i.e. they don't escape.Increasing s speeds up the iteration (points go farther on each step) so points escape faster consequently the black regions shrink as s increases.Increase/decrease s and watch what happens. NOTE: to get back to the original image you need to select (10b EMap) again. View/Sys/Gal: System "(10b EMap) a = .00; b = 1.00; c = 5.00; s = .60; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = .00; b = 1.00; c = 5.00; s = .60;."Range: (vMax,vMin) = (3.215,1.725), (hMin,hMax) = (-0.671,0.671)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = .00; b = 1.00; c = 5.00; s = .60; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = .00; b = 1.00; c = 5.00; s = .60; View/Sys/Gal: EMap "(10b EMap) a = 3.50; b = 1.30; c = .90; s = .87;" in "HopalongEMaps."Range: (vMax,vMin) = (7.294,-2.706), (hMin,hMax) = (-3.428,6.572)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.50; b = 1.30; c = .90; s = .87; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.50; b = 1.30; c = .90; s = .87; View/Sys/Gal: EMap "(10b EMap) a = 3.50; b = 1.30; c = .90; s = 1.80;" in "HopalongEMaps."Range: (vMax,vMin) = (4.826,2.679), (hMin,hMax) = (1.246,3.283)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.50; b = 1.30; c = .90; s = 1.80; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.50; b = 1.30; c = .90; s = 1.80; View/Sys/Gal: EMap "(10b EMap) a = 3.60; b = -3.80; c = 2.90; s = 1.50;" in "HopalongEMaps."Range: (vMax,vMin) = (6.029,0.314), (hMin,hMax) = (-1.574,3.270)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.60; b = -3.80; c = 2.90; s = 1.50; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.60; b = -3.80; c = 2.90; s = 1.50; View/Sys/Gal: System "(10b EMap) a = 3.70; b = 1.70; c = -1.00; s = 2.40; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = 3.70; b = 1.70; c = -1.00; s = 2.40;."Range: (vMax,vMin) = (7.900,-2.100), (hMin,hMax) = (-3.478,6.522)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.70; b = 1.70; c = -1.00; s = 2.40; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.70; b = 1.70; c = -1.00; s = 2.40; View/Sys/Gal: System "(10b EMap) a = 3.800; b = .580; c = 1.900; s = 4.200; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = 3.800; b = .580; c = 1.900; s = 4.200;."Range: (vMax,vMin) = (3.047,1.797), (hMin,hMax) = (0.836,2.086)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.800; b = .580; c = 1.900; s = 4.200; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.800; b = .580; c = 1.900; s = 4.200; View/Sys/Gal: System "(10b EMap) a = 3.800; b = .590; c = .900; s = .260; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = 3.800; b = .590; c = .900; s = .260;."Range: (vMax,vMin) = (4.440,3.088), (hMin,hMax) = (1.974,3.034)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.800; b = .590; c = .900; s = .260; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.800; b = .590; c = .900; s = .260; View/Sys/Gal: System "(10b EMap) a = 3.80; b = .58; c = 1.90; s = 2.70; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = 3.80; b = .58; c = 1.90; s = 2.70;."Range: (vMax,vMin) = (7.290,-2.710), (hMin,hMax) = (-3.430,6.570)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.80; b = .58; c = 1.90; s = 2.70; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.80; b = .58; c = 1.90; s = 2.70; View/Sys/Gal: System "(10b EMap) a = 3.80; b = .59; c = .90; s = -.26; ," in gallery "HopalongEMaps," renamed as "(10b EMap) a = 3.80; b = .59; c = .90; s = -.26;."Range: (vMax,vMin) = (5.499,4.548), (hMin,hMax) = (2.205,3.018)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.80; b = .59; c = .90; s = -.26; This iteration is defined by:x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.80; b = .59; c = .90; s = -.26;This image makes a nice shifted-pattern quilt.To see the quilt image, shift right click in the graphics area. View/Sys/Gal: System "(11 EMap) a = 4.90; b = -.23; c = -.33; d = -83.00; ," in gallery "HopalongEMaps," renamed as "(11 EMap) a = 4.90; b = -.23; c = -.33; d = -83.00;."Range: (vMax,vMin) = (1.700,0.450), (hMin,hMax) = (3.864,5.114)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.23; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.23; c = -.33; d = -83.00; View/Sys/Gal: EMap "(12 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00;" in "HopalongEMaps."Range: (vMax,vMin) = (1.763,0.540), (hMin,hMax) = (3.927,5.177)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.12; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.12; c = -.33; d = -83.00;This makes another nice shifted-pattern quilt. View/Sys/Gal: EMap "(13 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00;" in "HopalongEMaps."Range: (vMax,vMin) = (2.260,-0.240), (hMin,hMax) = (3.051,5.509)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.12; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.12; c = -.33; d = -83.00; View/Sys/Gal: System "(14 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00; ," in gallery "HopalongEMaps," renamed as "(14 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00;."Range: (vMax,vMin) = (7.000,-2.000), (hMin,hMax) = (-2.220,6.800)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.12; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.12; c = -.33; d = -83.00; View/Sys/Gal: System "(15 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00; ," in gallery "HopalongEMaps," renamed as "(15 EMap) a = 4.90; b = -.12; c = -.33; d = -83.00;."Range: (vMax,vMin) = (4.140,-0.860), (hMin,hMax) = (0.990,5.990)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.12; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.12; c = -.33; d = -83.00; View/Sys/Gal: EMap "(16 EMap) a = 4.70; b = -.12; c = -.31; d = -81.00;" in "HopalongEMaps."Range: (vMax,vMin) = (2.368,-1.108), (hMin,hMax) = (2.843,5.857)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.70; b = -.12; c = -.31; d = -81.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.70; b = -.12; c = -.31; d = -81.00; View/Sys/Gal: EMap "(17 EMap) a = 4.90; b = -.14; c = -.33; d = -83.00;" in "HopalongEMaps."Range: (vMax,vMin) = (7.000,-2.000), (hMin,hMax) = (-2.220,6.800)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.14; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.14; c = -.33; d = -83.00; View/Sys/Gal: EMap "(18 EMap) a = 4.90; b = -.13; c = -.33; d = -83.00;" in "HopalongEMaps."Range: (vMax,vMin) = (7.000,-2.000), (hMin,hMax) = (-2.220,6.800)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.13; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.13; c = -.33; d = -83.00; View/Sys/Gal: System "(19 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00; ," in gallery "HopalongEMaps," renamed as "(19 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00;."Range: (vMax,vMin) = (15.536,6.536), (hMin,hMax) = (591.883,600.903)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.13; c = -.33; d = 9.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.13; c = -.33; d = 9.00; View/Sys/Gal: System "(20 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00; ," in gallery "HopalongEMaps," renamed as "(20 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00;."Range: (vMax,vMin) = (29.040,-6.960), (hMin,hMax) = (583.000,620.000)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.13; c = -.33; d = 9.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.13; c = -.33; d = 9.00;This is the previous system zoomed out. The main part of the graphic just repeats forever. View/Sys/Gal: System "(21 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00; ," in gallery "HopalongEMaps," renamed as "(21 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00;."Range: (vMax,vMin) = (11.317,7.329), (hMin,hMax) = (596.169,599.940)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.13; c = -.33; d = 9.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.13; c = -.33; d = 9.00; View/Sys/Gal: EMap "(22 EMap) a = 4.90; b = -.14; c = -.33; d = -83.00;" in "HopalongEMaps."Range: (vMax,vMin) = (6.630,3.600), (hMin,hMax) = (2.730,6.130)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.14; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.14; c = -.33; d = -83.00; View/Sys/Gal: System "(23 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00; ," in gallery "HopalongEMaps," renamed as "(23 EMap) a = 5.00; b = -.13; c = -.33; d = 9.00;."Range: (vMax,vMin) = (10.021,8.027), (hMin,hMax) = (597.206,599.092)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.13; c = -.33; d = 9.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.13; c = -.33; d = 9.00; View/Sys/Gal: EMap "(24 EMap) a = 4.90; b = -.14; c = -.34; d = 5.20;" in "HopalongEMaps."Range: (vMax,vMin) = (13.465,9.477), (hMin,hMax) = (596.117,599.888)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.14; c = -.34; d = 5.20; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.14; c = -.34; d = 5.20; View/Sys/Gal: EMap "(25 EMap) a = 5.00; b = -.24; c = -.37; d = -10.00;" in "HopalongEMaps."Range: (vMax,vMin) = (2.187,-0.243), (hMin,hMax) = (3.488,5.528)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.24; c = -.37; d = -10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.24; c = -.37; d = -10.00; View/Sys/Gal: System "(26 EMap) a = 4.90; b = -.14; c = -.35; d = 5.50; ," in gallery "HopalongEMaps," renamed as "(26 EMap) a = 4.90; b = -.14; c = -.35; d = 5.50;."Range: (vMax,vMin) = (13.544,9.556), (hMin,hMax) = (597.616,601.387)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.14; c = -.35; d = 5.50; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.14; c = -.35; d = 5.50; View/Sys/Gal: System "(27 EMap) a = 4.90; b = -.13; c = -.35; d = 5.50; ," in gallery "HopalongEMaps," renamed as "(27 EMap) a = 4.90; b = -.13; c = -.35; d = 5.50;."Range: (vMax,vMin) = (15.402,11.414), (hMin,hMax) = (597.224,600.995)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.13; c = -.35; d = 5.50; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.13; c = -.35; d = 5.50; View/Sys/Gal: System "(28 EMap) a = 4.90; b = -.14; c = -.35; d = 5.50; ," in gallery "HopalongEMaps," renamed as "(28 EMap) a = 4.90; b = -.14; c = -.35; d = 5.50;."Range: (vMax,vMin) = (13.321,9.333), (hMin,hMax) = (597.197,600.968)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.14; c = -.35; d = 5.50; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.14; c = -.35; d = 5.50; View/Sys/Gal: EMap "(28b EMap)" in "HopalongEMaps."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=0This is a time-scaled version of (28).By increasing s you can decrease the amount of black in the image. View/Sys/Gal: EMap "(28b EMap) a = 4.90; b = -.14; c = -.35; d = 5.50; s = .88;" in "HopalongEMaps."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; View/Sys/Gal: EMap "(28b EMap) a = 4.90; b = -.14; c = -.36; d = 5.60; s = .46;" in "HopalongEMaps."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; View/Sys/Gal: System "(28b EMap) a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90; ," in gallery "HopalongEMaps," renamed as "(28b EMap) a = 5.30; b = -.18; c = -.41; d = 5.10; s = 2.90;."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; View/Sys/Gal: System "(28b EMap) a = 5.60; b = -.17; c = -.22; d = 5.10; s = 2.90; ," in gallery "HopalongEMaps," renamed as "(28b EMap) a = 5.60; b = -.17; c = -.22; d = 5.10; s = 2.90;."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; View/Sys/Gal: EMap "(28b EMap) a = 5.60; b = -.17; c = -.40; d = 5.10; s = 2.90;" in "HopalongEMaps."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; View/Sys/Gal: EMap "new 10 EMapCT7" in "HopalongEMaps."Range: (vMax,vMin) = (4.256,3.348), (hMin,hMax) = (2.365,3.224)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.80; b = .58; c = 1.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.80; b = .58; c = 1.00; EMap CT: 7 View/Sys/Gal: EMap "new 10b EMapCT3" in "HopalongEMaps."Range: (vMax,vMin) = (4.096,2.644), (hMin,hMax) = (1.081,2.315)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 2.5000; b = 1.4000; c = .9100; s = 5.4000; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 2.5000; b = 1.4000; c = .9100;         s = 5.4000; EMap CT: 3 View/Sys/Gal: EMap "new 10b EMapMaxCT2" in "HopalongEMaps."Range: (vMax,vMin) = (4.440,3.088), (hMin,hMax) = (1.974,3.034)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.800; b = .590; c = .900; s = .260; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.800; b = .590; c = .900;         s = .260; EMap CT: 2 View/Sys/Gal: EMap "new 10b EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (5.499,4.548), (hMin,hMax) = (2.205,3.018)VFld: ((1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+s*.01)*(a-x)), a = 3.80; b = .59; c = .90; s = -.26; This iteration is defined by:        x <- (1+s*.01)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+s*.01)*(a-x).Parameters are:         a = 3.80; b = .59; c = .90;         s = -.26; EMap CT: 3 View/Sys/Gal: EMap "new 11 EMapCT3" in "HopalongEMaps."Range: (vMax,vMin) = (0.887,-0.418), (hMin,hMax) = (4.548,5.560)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.7000; b = -.2100; c = -.5100; d = -9.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.7000; b = -.2100; c = -.5100;         d = -9.0000; EMap CT: 3 View/Sys/Gal: EMap "new 12 EMapMaxCT1" in "HopalongEMaps."Range: (vMax,vMin) = (1.736,1.390), (hMin,hMax) = (4.706,5.051)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.90; b = -.12; c = -.33; d = -83.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.90; b = -.12; c = -.33; d = -83.00; EMap CT: 1 View/Sys/Gal: EMap "new 17 EMapCT1" in "HopalongEMaps."Range: (vMax,vMin) = (4.395,3.500), (hMin,hMax) = (2.454,3.256)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.9000; b = -.1400; c = -.3400; d = -69.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.9000; b = -.1400; c = -.3400;         d = -69.0000; EMap CT: 1 View/Sys/Gal: EMap "new 18 EMapCT0" in "HopalongEMaps."Range: (vMax,vMin) = (5.018,3.851), (hMin,hMax) = (3.431,4.538)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.9000; b = -.1300; c = -.3400; d = -5.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.9000; b = -.1300; c = -.3400;         d = -5.0000; EMap CT: 0 View/Sys/Gal: EMap "new 2 EMapCT0" in "HopalongEMaps."Range: (vMax,vMin) = (0.888,-1.316), (hMin,hMax) = (-7.239,-5.153)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .00; b = -.93; c = 5.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .00; b = -.93; c = 5.00; EMap CT: 0 View/Sys/Gal: EMap "new 25 EMapMaxCT0" in "HopalongEMaps."Range: (vMax,vMin) = (1.912,0.347), (hMin,hMax) = (3.428,4.800)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.00; b = -.24; c = -.37; d = -10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.00; b = -.24; c = -.37; d = -10.00; EMap CT: 0 View/Sys/Gal: EMap "new 3 EMapCT0" in "HopalongEMaps."Range: (vMax,vMin) = (-1.741,-2.350), (hMin,hMax) = (-1.135,-0.460)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .0000; b = .9000; c = 4.7000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .0000; b = .9000; c = 4.7000; EMap CT: 0 View/Sys/Gal: EMap "new 4 EMapCT2" in "HopalongEMaps."Range: (vMax,vMin) = (-1.945,-3.890), (hMin,hMax) = (3.773,5.613)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 1.00; b = 1.00; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 1.00; b = 1.00; c = 10.00; EMap CT: 2 View/Sys/Gal: EMap "new 5 EMapMaxCT2" in "HopalongEMaps."Range: (vMax,vMin) = (1.308,-0.097), (hMin,hMax) = (0.498,1.761)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 2.00; b = 2.10; c = 10.00; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 2.00; b = 2.10; c = 10.00; EMap CT: 2 View/Sys/Gal: EMap "new 6 EMapCT0" in "HopalongEMaps."Range: (vMax,vMin) = (5.099,4.256), (hMin,hMax) = (3.267,4.064)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.70; b = .98; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.70; b = .98; c = 1.30; EMap CT: 0 View/Sys/Gal: EMap "new 8 EMapMaxCT8" in "HopalongEMaps."Range: (vMax,vMin) = (0.073,-1.150), (hMin,hMax) = (2.358,3.383)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.2000; b = .7800; c = 1.3000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.2000; b = .7800; c = 1.3000; EMap CT: 8 View/Sys/Gal: EMap "new 8b EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (1.880,0.908), (hMin,hMax) = (2.807,3.727)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.20; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.20; b = .70; c = 1.30; EMap CT: 3 View/Sys/Gal: EMap "new 8c EMapCT5" in "HopalongEMaps."Range: (vMax,vMin) = (4.489,2.415), (hMin,hMax) = (0.255,2.218)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.20; b = .70; c = 1.30; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.20; b = .70; c = 1.30; EMap CT: 5 View/Sys/Gal: EMap "new 9 EMapCT2" in "HopalongEMaps."Range: (vMax,vMin) = (6.356,4.376), (hMin,hMax) = (3.268,5.042)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 5.8000; b = .7100; c = 1.4000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 5.8000; b = .7100; c = 1.4000; EMap CT: 2 View/Sys/Gal: EMap "new* 11 EMapCT3" in "HopalongEMaps."Range: (vMax,vMin) = (-0.544,-1.466), (hMin,hMax) = (2.717,3.415)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.7000; b = -.1700; c = -.4100; d = -5.6000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.7000; b = -.1700; c = -.4100; d = -5.6000; EMap CT: 3 View/Sys/Gal: EMap "new* 11b EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (3.211,1.056), (hMin,hMax) = (4.789,6.418)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.7000; b = -.2100; c = -.4100; d = -5.6000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.7000; b = -.2100; c = -.4100;         d = -5.6000; EMap CT: 3 View/Sys/Gal: EMap "new* 11b w/s EMapCT2" in "HopalongEMaps."Range: (vMax,vMin) = (6.429,-3.571), (hMin,hMax) = (-4.190,5.810)VFld: ((1+.1*s)*(y-sgn(x)*sqrt(abs(b*x-c))),(1+.1*s)*(a-x%d)), a = 2.3000; b = -.2300; c = .3300; d = -8.9000; s = .2800; This iteration is defined by:        x <- (1+.1*s)*(y-sgn(x)*sqrt(abs(b*x-c))),        y <- (1+.1*s)*(a-x%d).Parameters are:         a = 2.3000; b = -.2300; c = .3300;         d = -8.9000; s = .2800; EMap CT: 2 View/Sys/Gal: EMap "new* 15 EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (0.085,-0.052), (hMin,hMax) = (3.120,3.245)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.9000; b = -.1200; c = -.3800; d = -6.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.9000; b = -.1200; c = -.3800;         d = -6.0000; EMap CT: 3 View/Sys/Gal: EMap "new* 16 EMapMaxCT5" in "HopalongEMaps."Range: (vMax,vMin) = (4.034,3.207), (hMin,hMax) = (3.332,4.018)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.7000; b = -.1200; c = -.3200; d = -43.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.7000; b = -.1200; c = -.3200;         d = -43.0000; EMap CT: 5 View/Sys/Gal: EMap "new* 17 EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (4.501,3.796), (hMin,hMax) = (3.384,5.000)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.6000; b = -.1400; c = -.3400; d = -69.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.6000; b = -.1400; c = -.3400;                 d = -69.0000; EMap CT: 3 View/Sys/Gal: EMap "new* 18 EMapMaxCT1" in "HopalongEMaps."Range: (vMax,vMin) = (5.018,3.851), (hMin,hMax) = (3.431,4.538)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 4.9000; b = -.1300; c = -.3400; d = -5.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 4.9000; b = -.1300; c = -.3400;         d = -5.0000; EMap CT: 1 View/Sys/Gal: EMap "new* 2 EMapMaxCT1" in "HopalongEMaps."Range: (vMax,vMin) = (0.000,-1.950), (hMin,hMax) = (-2.410,0.000)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .0000; b = -.9300; c = 5.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .0000; b = -.9300; c = 5.0000; EMap CT: 1 View/Sys/Gal: EMap "new* 22 EMapMaxCT5" in "HopalongEMaps."Range: (vMax,vMin) = (6.378,6.017), (hMin,hMax) = (4.490,4.650)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.2000; b = -.1400; c = -.3400; d = -69.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.2000; b = -.1400; c = -.3400;         d = -69.0000; EMap CT: 5 View/Sys/Gal: EMap "new* 25 EMapMaxCT0" in "HopalongEMaps."Range: (vMax,vMin) = (1.784,0.746), (hMin,hMax) = (3.363,4.252)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x%d), a = 5.0000; b = -.2400; c = -.4300; d = -10.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x%d.Parameters are:         a = 5.0000; b = -.2400; c = -.4300;         d = -10.0000; EMap CT: 0 View/Sys/Gal: EMap "new* 3 EMapCT0" in "HopalongEMaps."Range: (vMax,vMin) = (-2.149,-2.516), (hMin,hMax) = (-1.605,-1.209)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = .0062; b = .9000; c = 4.5000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = .0062; b = .9000; c = 4.5000; EMap CT: 0 View/Sys/Gal: EMap "new* 4 EMapCT5" in "HopalongEMaps."Range: (vMax,vMin) = (8.332,6.155), (hMin,hMax) = (2.855,4.868)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 1.0000; b = 1.0000; c = 10.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 1.0000; b = 1.0000; c = 10.0000; EMap CT: 5 View/Sys/Gal: EMap "new* 5 EMapMaxCT3" in "HopalongEMaps."Range: (vMax,vMin) = (1.282,-0.786), (hMin,hMax) = (0.846,2.660)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 2.1000; b = 2.1000; c = 10.0000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 2.1000; b = 2.1000; c = 10.0000; EMap CT: 3 View/Sys/Gal: EMap "new* 6 EMapCT1" in "HopalongEMaps."Range: (vMax,vMin) = (5.099,4.256), (hMin,hMax) = (3.307,4.104)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 3.7000; b = .9800; c = 1.3000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 3.7000; b = .9800; c = 1.3000; EMap CT: 1 View/Sys/Gal: EMap "new* 8 EMapMaxCT8" in "HopalongEMaps."Range: (vMax,vMin) = (1.212,0.541), (hMin,hMax) = (2.917,3.468)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.2000; b = .7800; c = 1.3000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.2000; b = .7800; c = 1.3000; EMap CT: 8 View/Sys/Gal: EMap "new* 8b EMapCT3" in "HopalongEMaps."Range: (vMax,vMin) = (6.475,5.171), (hMin,hMax) = (2.633,3.751)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.2000; b = .7000; c = 1.5000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.2000; b = .7000; c = 1.5000; EMap CT: 3 View/Sys/Gal: EMap "new* 8c EMapCT2" in "HopalongEMaps."Range: (vMax,vMin) = (4.756,3.562), (hMin,hMax) = (0.000,1.079)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 4.5000; b = .7000; c = 1.3000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 4.5000; b = .7000; c = 1.3000; EMap CT: 2 View/Sys/Gal: EMap "new* 9 EMapCT2" in "HopalongEMaps."Range: (vMax,vMin) = (6.267,4.353), (hMin,hMax) = (3.506,5.176)VFld: (y-sgn(x)*sqrt(abs(b*x-c)),a-x), a = 5.9000; b = .6700; c = 1.3000; This iteration is defined by:        x <- y-sgn(x)*sqrt(abs(b*x-c)),        y <- a-x.Parameters are:         a = 5.9000; b = .6700; c = 1.3000; EMap CT: 2