comment:

trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring) trappedPoint.Delta is the level: 0 - Steps-1

See the paper: "Evolution of Math into Art via Mobius Transformations" by Anne M. Burns, Department of Mathematics, Long Island University. http://myweb.cwpost.liu.edu/aburns/

Also, see pages 88-89 in the book: "Indra's Pearls, The Vision of Felix Klein" by David Mumford, Caroline Series, David Wright. http://klein.math.okstate.edu/IndrasPearls/

global:

Complex ShowCenter[] = LC1,LC2,LC3,LC4,LC5,LC6,LC7,LC8,LC9,LC10,LC11,LC12,LC13,LC14,LC15,LC16 Complex ShowRing[] = LR1,LR2,LR3,LR4,LR5,LR6,LR7,LR8,LR9,LR10,LR11,LR12,LR13,LR14,LR15,LR16 AbsV = Sqrt(AbsU^2 - 1) u = AbsU Cis(DegreeToRadian(ArgU)) v = AbsV Cis(DegreeToRadian(ArgV)) Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u))

totalGen = 1 + N + 52 Mobius m[totalGen]

' ' Given N, find radius R such that N circles with radius R can be ' placed along the inside of the unit circle, each tangent to the ' unit circle and each of its two adjacent neighbors. ' r = 1/(1+1/Sin(Math.PI/N))

step = 2Math.PI/N ang = IIf(Shift, step/2, 0) ' ' Center generator (index 0) ' m[0] = Mobius(1-2r, 0, 0, 1) ' ' Ring generators (indices 1..N) ' for (i = 1, i <= N, i += 1) { rotate = Cis(ang) m[i] = Mobius.Multiply( \ Mobius(rrotate, (1-r)rotate, 0, 1), \ UnitCircleGroup \ ) ang += step } ' ' Custom generators (keep if needed – they increase totalGen) ' m[N+1]=Mobius(0.085786442,Complex( 0.292893222, 0.292893222),0,1) m[N+2]=Mobius(0.085786442,Complex(-0.292893222,-0.292893222),0,1) m[N+3]=Mobius(0.085786442,Complex( 0.292893222,-0.292893222),0,1) m[N+4]=Mobius(0.085786442,Complex(-0.292893222, 0.292893222),0,1)

'm[N+5]=Mobius(0.022407752,Complex( 0.076504842, 0.076504842), 0, 1) 'm[N+6]=Mobius(0.022407752,Complex(-0.076504842, -0.076504842), 0, 1) 'm[N+7]=Mobius(0.022407752,Complex( 0.076504842, -0.076504842), 0, 1) 'm[N+8]=Mobius(0.022407752,Complex(-0.076504842, 0.076504842), 0, 1)

m[N+5]=Mobius(0.041421362,Complex(0.400000002,0.224264072), 0, 1) m[N+6]=Mobius(0.041421362,Complex(0.224264072,0.400000002), 0, 1)

m[N+7]=Mobius(0.041421362,Complex(-0.400000002,0.224264072), 0, 1) m[N+8]=Mobius(0.041421362,Complex(-0.224264072,0.400000002), 0, 1)

m[N+9]=Mobius(0.041421362,Complex(-0.400000002,-0.224264072), 0, 1) m[N+10]=Mobius(0.041421362,Complex(-0.224264072,-0.400000002), 0, 1)

m[N+11]=Mobius(0.041421362,Complex(0.400000002,-0.224264072), 0, 1) m[N+12]=Mobius(0.041421362,Complex(0.224264072,-0.400000002), 0, 1)

m[N+13]=Mobius(0.023649462,Complex(0.442905162,0.175342122), 0, 1) m[N+14]=Mobius(0.023649462,Complex(0.175342122,0.442905162), 0, 1)

m[N+15]=Mobius(0.023649462,Complex(-0.442905162,0.175342122), 0, 1) m[N+16]=Mobius(0.023649462,Complex(-0.175342122,0.442905162), 0, 1)

m[N+17]=Mobius(0.023649462,Complex(-0.442905162,-0.175342122), 0, 1) m[N+18]=Mobius(0.023649462,Complex(-0.175342122,-0.442905162), 0, 1)

m[N+19]=Mobius(0.023649462,Complex(0.442905162,-0.175342122), 0, 1) m[N+20]=Mobius(0.023649462,Complex(0.175342122,-0.442905162), 0, 1)

m[N+21]=Mobius(0.015132432,Complex(0.463467092,0.142459882), 0, 1) m[N+22]=Mobius(0.015132432,Complex(0.142459882,0.463467092), 0, 1)

m[N+23]=Mobius(0.015132432,Complex(-0.463467092,0.142459882), 0, 1) m[N+24]=Mobius(0.015132432,Complex(-0.142459882,0.463467092), 0, 1)

m[N+25]=Mobius(0.015132432,Complex(-0.463467092,-0.142459882), 0, 1) m[N+26]=Mobius(0.015132432,Complex(-0.142459882,-0.463467092), 0, 1)

m[N+27]=Mobius(0.015132432,Complex(0.463467092,-0.142459882), 0, 1) m[N+28]=Mobius(0.015132432,Complex(0.142459882,-0.463467092), 0, 1)

m[N+29]=Mobius(0.010466922,Complex(0.474730622,0.119471642), 0, 1) m[N+30]=Mobius(0.010466922,Complex(0.119471642,0.474730622), 0, 1)

m[N+31]=Mobius(0.010466922,Complex(-0.474730622,0.119471642), 0, 1) m[N+32]=Mobius(0.010466922,Complex(-0.119471642,0.474730622), 0, 1)

m[N+33]=Mobius(0.010466922,Complex(-0.474730622,-0.119471642), 0, 1) m[N+34]=Mobius(0.010466922,Complex(-0.119471642,-0.474730622), 0, 1)

m[N+35]=Mobius(0.010466922,Complex(0.474730622,-0.119471642), 0, 1) m[N+36]=Mobius(0.010466922,Complex(0.119471642,-0.474730622), 0, 1)

m[N+37]=Mobius(0.007653932,Complex(0.481521772,0.102671482), 0, 1) m[N+38]=Mobius(0.007653932,Complex(0.102671482,0.481521772), 0, 1)

m[N+39]=Mobius(0.007653932,Complex(-0.481521772,0.102671482), 0, 1) m[N+40]=Mobius(0.007653932,Complex(-0.102671482,0.481521772), 0, 1)

m[N+41]=Mobius(0.007653932,Complex(-0.481521772,-0.102671482), 0, 1) m[N+42]=Mobius(0.007653932,Complex(-0.102671482,-0.481521772), 0, 1)

m[N+43]=Mobius(0.007653932,Complex(0.481521772,-0.102671482), 0, 1) m[N+44]=Mobius(0.007653932,Complex(0.102671482,-0.481521772), 0, 1)

m[N+45]=Mobius(0.005833582,Complex(0.485916492,0.089920032), 0, 1) m[N+46]=Mobius(0.005833582,Complex(0.089920032,0.485916492), 0, 1)

m[N+47]=Mobius(0.005833582,Complex(-0.485916492,0.089920032), 0, 1) m[N+48]=Mobius(0.005833582,Complex(-0.089920032,0.485916492), 0, 1)

m[N+49]=Mobius(0.005833582,Complex(-0.485916492,-0.089920032), 0, 1) m[N+50]=Mobius(0.005833582,Complex(-0.089920032,-0.485916492), 0, 1)

m[N+51]=Mobius(0.005833582,Complex(0.485916492,-0.089920032), 0, 1) m[N+52]=Mobius(0.005833582,Complex(0.089920032,-0.485916492), 0, 1)

' ' ---- Compute maximum possible number of center circles ---- ' Complex MaxTotal = 0 count = 1 ' at level 0, only the center circle for (i = 0, i < Steps, i += 1) { MaxTotal += count count *= totalGen } ' ' Allocate arrays of size MaxTotal ' Complex Total = MaxTotal ' will be overwritten with actual count after generation Circle c[Total] Complex index[Total] Complex level[Total] Circle UnitCircle = CircleC(0, 1) ' ' ---- Generate only center circles ---- ' ' Initialize level 0: the single center circle c[0] = Mobius.TransformCircle(m[0], UnitCircle) index[0] = 0 level[0] = 0 count = 1 start = 0 end = 1 ' circles from previous level are at indices start..end-1

if (Steps > 1) { for (lev = 1, lev < Steps, lev += 1) { for (j = start, j < end, j += 1) { ' All circles in the array have index = 0, so no need to check. ' Apply all generators to each existing center circle. for (k = 0, k < totalGen, k += 1) { c[count] = Mobius.TransformCircle(m[k], c[j]) if (c[count].Radius >= RadiusMin) { index[count] = 0 ' inherited from parent (always 0) level[count] = lev count += 1 } } } start = end end = count ' new circles for next level start at the old end } } Total = count ' actual number used

CurveTrap.Initialize( \ Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \ ) ' ' Add the circles to the trap. ' for (i = 0, i < Total, i += 1) { lev = level[i] idx = index[i] ' always 0 now if (idx = 0) { if (ShowCenter[lev]) { CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) } } else { ' This branch will never be taken because we only have idx=0 if (ShowRing[lev]) { CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) } } }

trap:

trappedPoint = CurveTrap.Apply(z)

properties:

divider { caption = "General Options" } option Center { type = Complex caption = "Center" details = "Center of trap" default = 0 } option Angle { type = Float caption = "Angle" details = "Angle of rotation" default = 0 range = [-360,360] } option Scale { type = Float caption = "Scale" details = "Scale factor applied to trap" range = (0,) default = 2 } option Solid { type = Boolean caption = "Solid" details = "Check to create solid trap" default = False } option AlternateAngle { type = Boolean caption = "Alternate Angle" details = "Use alternate angle calculation" default = False } option LineWidth { type = Float caption = "Line Width" details = "Extent of trap on either side of curve (> 0)" range = (0,) default = 0.00411522633744855967078189300413 enabled = ~Solid } divider { caption = "U/V Controls" } option AbsU { type = Float caption = "Abs(U)" details = "Magnitude of U (1-2)" default = 1.1 range = [1,2] } option ArgU { type = Float caption = "Arg(U)" details = "Angle of U" default = 0 range = [-360,360] } option ArgV { type = Float caption = "Arg(V)" details = "Angle of V" default = 180 range = [-360,360] } divider { caption = "Circle Controls" } option N { type = IntegerEnum(3,12) caption = "N" details = "Number of base circles" default = 4 } option Steps { type = IntegerEnum(1,16) caption = "Steps" details = "Number of inversion steps" default = 4 ' you can increase to 7 now, but set RadiusMin > 0 to avoid memory issues } option Shift { type = Boolean caption = "Shift" details = "Check to rotate initial chain by pi/N" default = False } option RadiusMin { type = Float caption = "Radius Min" details = "Minimum acceptable circle radius" default = 0.001 ' set to a small positive value to prune tiny circles range = [0,) }

define ShowLevel(Index)

divider { caption = "Level #Index# Options" } option LR#Index# { type = Boolean caption = "Show Ring" details = "Show ring of circles at level #Index#" default = True enabled = Steps >= #Index# } option LC#Index# { type = Boolean caption = "Show Center" details = "Show center circle at level #Index#" default = True enabled = Steps >= #Index# }

end

include ShowLevel("1")

include ShowLevel("2")

include ShowLevel("3")

include ShowLevel("4")

include ShowLevel("5")

include ShowLevel("6")

include ShowLevel("7")

include ShowLevel("8")

include ShowLevel("9")

include ShowLevel("10")

include ShowLevel("11")

include ShowLevel("12")

include ShowLevel("13")

include ShowLevel("14")

include ShowLevel("15")

include ShowLevel("16")

comment:

trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring) trappedPoint.Delta is the level: 0 - Steps-1

See the paper: "Evolution of Math into Art via Mobius Transformations" by Anne M. Burns, Department of Mathematics, Long Island University. http://myweb.cwpost.liu.edu/aburns/

Also, see pages 88-89 in the book: "Indra's Pearls, The Vision of Felix Klein" by David Mumford, Caroline Series, David Wright. http://klein.math.okstate.edu/IndrasPearls/

global:

Complex ShowCenter[] = LC1,LC2,LC3,LC4,LC5,LC6,LC7,LC8,LC9,LC10,LC11,LC12,LC13,LC14,LC15,LC16 Complex ShowRing[] = LR1,LR2,LR3,LR4,LR5,LR6,LR7,LR8,LR9,LR10,LR11,LR12,LR13,LR14,LR15,LR16 AbsV = Sqrt(AbsU^2 - 1) u = AbsU Cis(DegreeToRadian(ArgU)) v = AbsV Cis(DegreeToRadian(ArgV)) Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u))

totalGen = 1 + N + 32 Mobius m[totalGen] ' ' Given N, find radius R such that N circles with radius R can be ' placed along the inside of the unit circle, each tangent to the ' unit circle and each of its two adjacent neighbors. ' r = 1/(1+1/Sin(Math.PI/N))

step = 2Math.PI/N ang = IIf(Shift, step/2, 0) ' ' Center generator (index 0) ' m[0] = Mobius(1-2r, 0, 0, 1) ' ' Ring generators (indices 1..N) ' for (i = 1, i <= N, i += 1) { rotate = Cis(ang) m[i] = Mobius.Multiply( \ Mobius(rrotate, (1-r)rotate, 0, 1), \ UnitCircleGroup \ ) ang += step } ' ' Custom generators ' m[N+1]=Mobius(0.085786442,Complex( 0.292893222, 0.292893222),0,1) m[N+2]=Mobius(0.085786442,Complex(-0.292893222,-0.292893222),0,1) m[N+3]=Mobius(0.085786442,Complex( 0.292893222,-0.292893222),0,1) m[N+4]=Mobius(0.085786442,Complex(-0.292893222, 0.292893222),0,1)

m[N+5]=Mobius(0.022407752,Complex(0.216388382,0.216388382), 0, 1) m[N+6]=Mobius(0.022407752,Complex(-0.216388382,0.216388382), 0, 1) m[N+7]=Mobius(0.022407752,Complex(-0.216388382,-0.216388382), 0, 1) m[N+8]=Mobius(0.022407752,Complex(0.216388382,-0.216388382), 0, 1)

m[N+9]=Mobius(0.041421362,Complex(0.400000002,0.224264072), 0, 1) m[N+10]=Mobius(0.041421362,Complex(0.224264072,0.400000002), 0, 1)

m[N+11]=Mobius(0.041421362,Complex(-0.400000002,0.224264072), 0, 1) m[N+12]=Mobius(0.041421362,Complex(-0.224264072,0.400000002), 0, 1)

m[N+13]=Mobius(0.041421362,Complex(-0.400000002,-0.224264072), 0, 1) m[N+14]=Mobius(0.041421362,Complex(-0.224264072,-0.400000002), 0, 1)

m[N+15]=Mobius(0.041421362,Complex(0.400000002,-0.224264072), 0, 1) m[N+16]=Mobius(0.041421362,Complex(0.224264072,-0.400000002), 0, 1)

m[N+17]=Mobius(0.022407752,Complex( 0.076504842, 0.076504842), 0, 1) m[N+18]=Mobius(0.022407752,Complex(-0.076504842, -0.076504842), 0, 1) m[N+19]=Mobius(0.022407752,Complex( 0.076504842, -0.076504842), 0, 1) m[N+20]=Mobius(0.022407752,Complex(-0.076504842, 0.076504842), 0, 1)

m[N+21]=Mobius(0.010318672,Complex(0.099645922, 0.099645922), 0, 1) m[N+22]=Mobius(0.008518112,Complex(0.082258122, 0.046118852), 0, 1) m[N+23]=Mobius(0.008518112,Complex(0.046118852, 0.08225812*2), 0, 1)

m[N+24]=Mobius(0.010318672,Complex(-0.099645922, 0.099645922), 0, 1) m[N+25]=Mobius(0.008518112,Complex(-0.082258122, 0.046118852), 0, 1) m[N+26]=Mobius(0.008518112,Complex(-0.046118852, 0.08225812*2), 0, 1)

m[N+27]=Mobius(0.010318672,Complex(-0.099645922, -0.099645922), 0, 1) m[N+28]=Mobius(0.008518112,Complex(-0.082258122, -0.046118852), 0, 1) m[N+29]=Mobius(0.008518112,Complex(-0.046118852, -0.08225812*2), 0, 1)

m[N+30]=Mobius(0.010318672,Complex(0.099645922, -0.099645922), 0, 1) m[N+31]=Mobius(0.008518112,Complex(0.082258122, -0.046118852), 0, 1) m[N+32]=Mobius(0.008518112,Complex(0.046118852, -0.08225812*2), 0, 1)

' ' Assign Total = the total number of circles. ' const Complex Total = 0 count = totalGen

for (i = 0, i < Steps, i += 1) { Total += count count *= totalGen } const Circle c[Total] const Complex index[Total] const Complex level[Total] Circle UnitCircle = CircleC(0, 1) ' ' Generate the base circles (all generators applied to unit circle) ' for (i = 0, i < totalGen, i += 1) { c[i] = Mobius.TransformCircle(m[i], UnitCircle) index[i] = i level[i] = 0 } count = totalGen max = 0 ' ' Generate the remaining circles by applying all generators iteratively. ' if (Steps > 1) { for (i = 1, i < Steps, i += 1) { min = max max = count

for (j = min, j < max, j += 1) { for (k = 0, k < totalGen, k += 1) { c[count] = Mobius.TransformCircle(m[k], c[j]) if (c[count].Radius >= RadiusMin) { index[count] = index[j] level[count] = i count += 1 } } } } } Total = count

CurveTrap.Initialize( \ Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \ ) ' ' Add the circles to the trap. ' for (i = 0, i < Total, i += 1) { lev = level[i] idx = index[i] if (idx = 0) { if (ShowCenter[lev]) { CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) } } else { if (ShowRing[lev]) { CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) } } }

trap:

trappedPoint = CurveTrap.Apply(z)

properties:

divider { caption = "General Options" } option Center { type = Complex caption = "Center" details = "Center of trap" default = 0 } option Angle { type = Float caption = "Angle" details = "Angle of rotation" default = 0 range = [-360,360] } option Scale { type = Float caption = "Scale" details = "Scale factor applied to trap" range = (0,) default = 2 } option Solid { type = Boolean caption = "Solid" details = "Check to create solid trap" default = False } option AlternateAngle { type = Boolean caption = "Alternate Angle" details = "Use alternate angle calculation" default = False } option LineWidth { type = Float caption = "Line Width" details = "Extent of trap on either side of curve (> 0)" range = (0,) default = 0.00411522633744855967078189300413 enabled = ~Solid } divider { caption = "U/V Controls" } option AbsU { type = Float caption = "Abs(U)" details = "Magnitude of U (1-2)" default = 1.1 range = [1,2] } option ArgU { type = Float caption = "Arg(U)" details = "Angle of U" default = 0 range = [-360,360] } option ArgV { type = Float caption = "Arg(V)" details = "Angle of V" default = 180 range = [-360,360] } divider { caption = "Circle Controls" } option N { type = IntegerEnum(3,12) caption = "N" details = "Number of base circles" default = 4 } option Steps { type = IntegerEnum(1,16) caption = "Steps" details = "Number of inversion steps" default = 4 ' <-- REDUCED from 8 to 4 to avoid memory crash } option Shift { type = Boolean caption = "Shift" details = "Check to rotate initial chain by pi/N" default = False } option RadiusMin { type = Float caption = "Radius Min" details = "Minimum acceptable circle radius" default = 0 range = [0,) }

define ShowLevel(Index)

divider { caption = "Level #Index# Options" } option LR#Index# { type = Boolean caption = "Show Ring" details = "Show ring of circles at level #Index#" default = True enabled = Steps >= #Index# } option LC#Index# { type = Boolean caption = "Show Center" details = "Show center circle at level #Index#" default = True enabled = Steps >= #Index# }

end

include ShowLevel("1")

include ShowLevel("2")

include ShowLevel("3")

include ShowLevel("4")

include ShowLevel("5")

include ShowLevel("6")

include ShowLevel("7")

include ShowLevel("8")

include ShowLevel("9")

include ShowLevel("10")

include ShowLevel("11")

include ShowLevel("12")

include ShowLevel("13")

include ShowLevel("14")

include ShowLevel("15")

include ShowLevel("16")

comment:

trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring) trappedPoint.Delta is the level: 0 - Steps-1

See the paper:

"Evolution of Math into Art via Mobius Transformations"

by Anne M. Burns, Department of Mathematics, Long Island University. http://myweb.cwpost.liu.edu/aburns/

Also, see pages 88-89 in the book:

"Indra's Pearls, The Vision of Felix Klein"

by David Mumford, Caroline Series, David Wright. http://klein.math.okstate.edu/IndrasPearls/

global:

Complex ShowCenter[] = LC1,LC2,LC3,LC4,LC5,LC6,LC7,LC8,LC9,LC10,LC11,LC12,LC13,LC14,LC15,LC16 Complex ShowRing[] = LR1,LR2,LR3,LR4,LR5,LR6,LR7,LR8,LR9,LR10,LR11,LR12,LR13,LR14,LR15,LR16 AbsV = Sqrt(AbsU^2 - 1) u = AbsU Cis(DegreeToRadian(ArgU)) v = AbsV Cis(DegreeToRadian(ArgV)) Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u))

' ========= ' DEFINE FOUR APOLLONIAN CIRCLES AS GENERATORS ' (scaled by 2 to match default trap Scale=2) ' ========= scaleFactor = 2 customRadius = 0.08578644 * scaleFactor

' Total generators = 1 (center) + N (ring) + 4 custom totalGen = 1 + N + 4 Mobius m[totalGen] ' ' Given N, find radius R such that N circles with radius R can be ' placed along the inside of the unit circle, each tangent to the ' unit circle and each of its two adjacent neighbors. ' r = 1/(1+1/Sin(Math.PI/N))

step = 2Math.PI/N ang = IIf(Shift, step/2, 0) ' ' Center generator (index 0) ' m[0] = Mobius(1-2r, 0, 0, 1) ' ' Ring generators (indices 1..N) ' for (i = 1, i <= N, i += 1) {

rotate = Cis(ang)
m[i] = Mobius.Multiply( \
  Mobius(r*rotate, (1-r)*rotate, 0, 1), \
  UnitCircleGroup \
)
ang += step

} ' ' Custom generators (indices N+1 .. N+4) ' m[N+1] = Mobius(customRadius, Complex( 0.29289322scaleFactor, 0.29289322scaleFactor), 0, 1) m[N+2] = Mobius(customRadius, Complex(-0.29289322scaleFactor, -0.29289322scaleFactor), 0, 1) m[N+3] = Mobius(customRadius, Complex( 0.29289322scaleFactor, -0.29289322scaleFactor), 0, 1) m[N+4] = Mobius(customRadius, Complex(-0.29289322scaleFactor, 0.29289322scaleFactor), 0, 1)

' ' Assign Total = the total number of circles. ' const Complex Total = 0 count = totalGen

for (i = 0, i < Steps, i += 1) {

Total += count
count *= totalGen

} const Circle c[Total] const Complex index[Total] const Complex level[Total] Circle UnitCircle = CircleC(0, 1) ' ' Generate the base circles (all generators applied to unit circle) ' for (i = 0, i < totalGen, i += 1) {

c[i] = Mobius.TransformCircle(m[i], UnitCircle)
index[i] = i
level[i] = 0

} count = totalGen max = 0 ' ' Generate the remaining circles by applying all generators iteratively. ' if (Steps > 1) {

for (i = 1, i < Steps, i += 1) {
  min = max
  max = count

for (j = min, j < max, j += 1) {

    for (k = 0, k < totalGen, k += 1) {
      c[count] = Mobius.TransformCircle(m[k], c[j])
      if (c[count].Radius >= RadiusMin) {
        index[count] = index[j]
        level[count] = i
        count += 1
      }
    }
  }
}

} Total = count

CurveTrap.Initialize( \

Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \

) ' ' Add the circles to the trap. ' for (i = 0, i < Total, i += 1) {

lev = level[i]
idx = index[i]
if (idx = 0) {
  if (ShowCenter[lev]) {
    CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev)
  }
} else {
  if (ShowRing[lev]) {
    CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev)
  }
}

}

trap:

trappedPoint = CurveTrap.Apply(z)

properties:

divider {

caption = "General Options"

} option Center {

type = Complex
caption = "Center"
details = "Center of trap"
default = 0

} option Angle {

type = Float
caption = "Angle"
details = "Angle of rotation"
default = 0
range = [-360,360]

} option Scale {

type = Float
caption = "Scale"
details = "Scale factor applied to trap"
range = (0,)
default = 2

} option Solid {

type = Boolean
caption = "Solid"
details = "Check to create solid trap"
default = False

} option AlternateAngle {

type = Boolean
caption = "Alternate Angle"
details = "Use alternate angle calculation"
default = False

} option LineWidth {

type = Float
caption = "Line Width"
details = "Extent of trap on either side of curve (> 0)"
range = (0,)
default = 0.00411522633744855967078189300413
enabled = ~Solid

} divider {

caption = "U/V Controls"

} option AbsU {

type = Float
caption = "Abs(U)"
details = "Magnitude of U (1-2)"
default = 1.1
range = [1,2]

} option ArgU {

type = Float
caption = "Arg(U)"
details = "Angle of U"
default = 0
range = [-360,360]

} option ArgV {

type = Float
caption = "Arg(V)"
details = "Angle of V"
default = 180
range = [-360,360]

} divider {

caption = "Circle Controls"

} option N {

type = IntegerEnum(3,12)
caption = "N"
details = "Number of base circles"
default = 4

} option Steps {

type = IntegerEnum(1,16)
caption = "Steps"
details = "Number of inversion steps"
default = 4   ' <-- REDUCED from 8 to 4 to avoid memory crash

} option Shift {

type = Boolean
caption = "Shift"
details = "Check to rotate initial chain by pi/N"
default = False

} option RadiusMin {

type = Float
caption = "Radius Min"
details = "Minimum acceptable circle radius"
default = 0
range = [0,)

}

#define ShowLevel(Index)

divider {

caption = "Level #Index# Options"

} option LR#Index# {

type = Boolean
caption = "Show Ring"
details = "Show ring of circles at level #Index#"
default = True
enabled = Steps >= #Index#

} option LC#Index# {

type = Boolean
caption = "Show Center"
details = "Show center circle at level #Index#"
default = True
enabled = Steps >= #Index#

}

#end #include ShowLevel("1") #include ShowLevel("2") #include ShowLevel("3") #include ShowLevel("4") #include ShowLevel("5") #include ShowLevel("6") #include ShowLevel("7") #include ShowLevel("8") #include ShowLevel("9") #include ShowLevel("10") #include ShowLevel("11") #include ShowLevel("12") #include ShowLevel("13") #include ShowLevel("14") #include ShowLevel("15") #include ShowLevel("16")