comment {
Brian's Formulae
}

bwp1 {
init:
  z = @InitValue
loop:
  z = z ^ @Exponent + @ZCoeff * z + #pixel    
bailout:
  |z| < @Bailout  
default:
  title = "BWP 01"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = 2
    min = 2
    max = 10
  endparam
  param ZCoeff
    caption = "Z Coefficient"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp2"
  Seed = #pixel
  Exponent = @Exponent
  ZCoeff = @ZCoeff
  Bailout = @Bailout
}

bwp2 {
init:
  z = #pixel
loop:
  z = z ^ @Exponent + @ZCoeff * z + @Seed    
bailout:
  |z| <= @bailout
default:
  title = "BWP 02"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = 2
    min = 2
    max = 10
  endparam
  param ZCoeff
    caption = "Z Coefficient"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp1"
  Exponent = @Exponent
  ZCoeff = @ZCoeff
  Bailout = @Bailout
}

bwp3 {
init:
  z1 = @InitValue
  t = #pixel
loop:
  z2 = z1
  z1 = sin(z1) - t
  t = 1 / (z1 * @Value)
  z = z1 - z2
bailout:
  |z| < @Bailout  
default:
  title = "BWP 03"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Value
    caption = "Value"
    default = (50, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp4 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = sin(z) - t
  t = 1 / (z * @Value)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 04"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Value
    caption = "Value"
    default = (50, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp5 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = sin(z) - t
  t = #pixel / (z * @Value)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 05"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Value
    caption = "Value"
    default = (50, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp6 {
init:
  z = @InitValue
loop:
  z = @Fun1(z) * @Fun2(z) + #pixel
bailout:
  |z| < @Bailout  
default:
  title = "BWP 06"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = sin()
  endfunc
switch:
  type = "bwp13"
  Seed = #pixel
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp7 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = tanh(z) - t
  t = 1 / (z * @Value)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 07"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Value
    caption = "Value"
    default = (50, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp8 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = sin(z) - t
  t = 1 / (z ^ @Exponent)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 08"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp9 {
init:
  z = @InitValue
loop:
  zs = z * z
  z = (zs + #pixel) / (1 + zs)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 09"
  param InitValue
    caption = "Initial Value"
    default = (-2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp10 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = @Fun(z) - t
  t = 1 / (z ^ @Exponent)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 10"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = sin()
  endfunc
}

bwp11 {
init:
  z = @InitValue
  t = (0, 0)
loop:
  z = z ^ @Exponent - t + #pixel
  t = 1 / @Fun(z)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 11"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = recip()
  endfunc
}

bwp12 {
init:
  z = @InitValue
loop:
  z = z ^ @Exponent + @FunZCoeff * @Fun(z) + #pixel    
bailout:
  |z| < @Bailout  
default:
  title = "BWP 12"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param FunZCoeff
    caption = "Fun(z) Coefficient"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = ident()
  endfunc
}

bwp13 {
init:
  z = #pixel
loop:
  z = @Fun1(z) * @Fun2(z) + @Seed    
bailout:
  |z| < @Bailout  
default:
  title = "BWP 13"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
switch:
  type = "bwp6"
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp14 {
init:
  z = @InitValue
loop:
  z = (z ^ @Exponent1) * (#pixel ^ @Exponent2) + #pixel    
bailout:
  |z| < @Bailout  
default:
  title = "BWP 14"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exponent2
    caption = "Exponent 2"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp15"
  Seed = #pixel
  Exponent1 = @Exponent1
  Exponent2 = @Exponent2
  Bailout = @Bailout
}

bwp15 {
init:
  z = #pixel
loop:
  z = (z ^ @Exponent1) * (@Seed ^ @Exponent2) + @Seed    
bailout:
  |z| <= @bailout
default:
  title = "BWP 15"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Exponent1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exponent2
    caption = "Exponent 2"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp14"
  Exponent1 = @Exponent1
  Exponent2 = @Exponent2
  Bailout = @Bailout
}

bwp16 {
init:
  z = @InitValue
loop:
  z = @Mult3 * ((@Mult1 * (z ^ @Exp1)) + \
  (@Mult2 * (z ^ @Exp2))) + @Fun(#pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 16"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = ident()
  endfunc
switch:
  type = "bwp17"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun = @Fun
  Bailout = @Bailout
}

bwp17 {
init:
  z = @Fun(#pixel)
loop:
  z = @Mult3 * ((@Mult1 * (z ^ @Exp1)) + \
  (@Mult2 * (z ^ @Exp2))) + @Fun(@Seed)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 17"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = ident()
  endfunc
switch:
  type = "bwp16"
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun = @Fun
  Bailout = @Bailout
}

bwp18 {
init:
  z = @InitValue
  int i = 0
loop:
  if ((i % 2) == 0)
    z = @Mult1 * (z ^ @Exp1)
  else
    z = @Mult2 * (z ^ @Exp2)
  endif
  z = z + @Fun(#pixel)
  i = i + 1
bailout:
  |z| < @Bailout  
default:
  title = "BWP 18"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (1, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = ident()
  endfunc
switch:
  type = "bwp19"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun = @Fun
  Bailout = @Bailout
}

bwp19 {
init:
  z = @Fun(#pixel)
  int i = 0
loop:
  if ((i % 2) == 0)
    z = @Mult1 * (z ^ @Exp1)
  else
    z = @Mult2 * (z ^ @Exp2)
  endif
  z = z + @Fun(@Seed)
  i = i + 1
bailout:
  |z| < @Bailout  
default:
  title = "BWP 19"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (1, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun
    caption = "Function"
    default = ident()
  endfunc
switch:
  type = "bwp18"
  Mult1 = @Mult1
  Mult2 = @Mult2
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun = @Fun
  Bailout = @Bailout
}

bwp20 {
init:
  c = #pixel
  z = sqrt((1 - c) / 6)
loop:
  zs = z * z
  z = zs * zs + (c - 1) * zs - c
bailout:
  |z| < @Bailout  
default:
  title = "BWP 20"
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp21"
  Seed = #pixel
  Bailout = @Bailout
}

bwp20a {
init:
  c = #pixel
  z = @InitValue
loop:
  zs = z * z
  z = zs * zs + (c - 1) * zs - c
bailout:
  |z| < @Bailout  
default:
  title = "BWP 20a"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp21"
  Seed = #pixel
  Bailout = @Bailout
}

bwp21 {
init:
  z = #pixel
loop:
  zs = z * z
  z = zs * zs + (@Seed - 1) * zs - @Seed
bailout:
  |z| < @Bailout  
default:
  title = "BWP 21"
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp20"
  Bailout = @Bailout
}

bwp22 {
; From PWC_Eqn_Mset and PWC_Eqn_Mset2 by Paul Carlson.

init:
  z = @InitValue

loop:
  z = (z^2 + #pixel) * (1 - z^2) / (1 + z^2) + @PixMult * #pixel

bailout:
  |z| < @Bailout

default:
  title = "BWP 22"
  maxiter = 1000

  param InitValue
    caption = "Initial Value"
    default = (0, 0)
    hint = "The initial value"
  endparam

  param PixMult
    caption = "Pixel multiplier"
    default = (0, 0)
    hint = "The pixel multiplier"
  endparam
    
  param Bailout
    caption = "Bailout Value"
    default = 1.0e20
    hint = "The bailout value."
  endparam

switch:
  type = "bwp23"
  Seed = #pixel
  PixMult = @PixMult
  Bailout = @Bailout
}

bwp23 {
; From PWC_Eqn_Mset and PWC_Eqn_Mset2 by Paul Carlson.

init:
  z = #pixel

loop:
  z = (z^2 + @Seed) * (1 - z^2) / (1 + z^2) + @PixMult * @Seed

bailout:
  |z| < @Bailout

default:
  title = "BWP 23"
  maxiter = 1000
    
  param Bailout
    caption = "Bailout Value"
    default = 1.0e20
    hint = "The bailout value."
  endparam

  param PixMult
    caption = "Pixel multiplier"
    default = (0, 0)
    hint = "The pixel multiplier"
  endparam

switch:
  type = "bwp22"
  PixMult = @PixMult
  Bailout = @Bailout
}

bwp24 {
init:
  z = @InitValue
loop:
  z = (z ^ @Exponent + #pixel) / (@Value + #pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 24"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Value
    caption = "Value"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp25"
  Seed = #pixel
  Exponent = @Exponent
  Value = @Value
  Bailout = @Bailout
}

bwp25 {
init:
  z = #pixel
loop:
  z = (z ^ @Exponent + @Seed) / (@Value + @Seed)
bailout:
  |z| <= @bailout
default:
  title = "BWP 25"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Value
    caption = "Value"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
switch:
  type = "bwp24"
  Exponent = @Exponent
  Value = @Value
  Bailout = @Bailout
}

bwp26 {
init:
  z = c = #pixel
loop:
  a = z ^ 3 + (c - 1) * z - c
  b = @Coeff1 * z ^ 2 + c - 1
  z = z - @Coeff2 * a / b
bailout:
  |z| <= @bailout
default:
  title = "BWP 26"
  param Coeff1
    caption = "Coefficient 1"
    default = (1, 0)
  endparam
  param Coeff2
    caption = "Coefficient 2"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
}

bwp27 {
init:
  z = @InitValue
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(#pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 27"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp28"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp28 {
init:
  z = @Fun4(#pixel)
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(@Seed)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 28"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp27"
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp29 {
init:
  z = @InitValue
loop:
  z = @Fun1((-z) ^ @Exponent) + @Fun2(@Offset + #pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 29"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Offset
    caption = "Offset"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
switch:
  type = "bwp30"
  Seed = #pixel
  Exponent = @Exponent
  Offset = @Offset
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp30 {
init:
  z = #pixel
loop:
  z = @Fun1((-z) ^ @Exponent) + @Fun2(@Offset + @Seed)
bailout:
  |z| <= @bailout
default:
  title = "BWP 30"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Offset
    caption = "Offset"
    default = (0, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
switch:
  type = "bwp29"
  Exponent = @Exponent
  Offset = @Offset
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp31 {
init:
  a = @Mult2
  b = @Exp2
  a = 1 / a
  b = 1 / b
  c = 1 / (@Exp2 - @Exp1)
  z = (-@Mult1 * @Exp1 * a * b) ^ c
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(#pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 31"
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp32"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp32 {
init:
  z = @Fun4(#pixel)
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(@Seed)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 32"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp31"
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp31n {
; A generalization of Jim Muth's MandelbrotMix4 formula
init:
  a = @Mult2
  b = @Exp2
  a = 1 / a
  b = 1 / b
  c = 1 / (@Exp2 - @Exp1)
  z = (-(@Mult1 * @Exp1 * a * b)) ^ c
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(#pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 31N"
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp32n"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp31nc {
; A generalization of Jim Muth's MandelbrotMix4 formula
init:
  a = @Mult2
  b = @Exp2
  a = 1 / a
  b = 1 / b
  c = 1 / (@Exp2 - @Exp1)
  z = conj((-(@Mult1 * @Exp1 * a * b)) ^ c)
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(#pixel)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 31NC"
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp32n"
  Seed = #pixel
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp32n {
init:
  z = @Fun4(#pixel)
loop:
  z = @Fun3(@Mult3 * (@Fun1(@Mult1 * (z ^ @Exp1)) + \
  @Fun2(@Mult2 * (z ^ @Exp2)))) + @Fun4(@Seed)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 32N"
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param Mult1
    caption = "Multiplier 1"
    default = (0.5, 0)
  endparam
  param Mult2
    caption = "Multiplier 2"
    default = (0.5, 0)
  endparam
  param Mult3
    caption = "Multiplier 3"
    default = (1, 0)
  endparam
  param Exp1
    caption = "Exponent 1"
    default = (2, 0)
  endparam
  param Exp2
    caption = "Exponent 2"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = ident()
  endfunc
  func Fun4
    caption = "Function 4"
    default = ident()
  endfunc
switch:
  type = "bwp31n"
  Mult1 = @Mult1
  Mult2 = @Mult2
  Mult3 = @Mult3
  Exp1 = @Exp1
  Exp2 = @Exp2
  Fun1 = @Fun1
  Fun2 = @Fun2
  Fun3 = @Fun3
  Fun4 = @Fun4
  Bailout = @Bailout
}

bwp33 {
init:
  z = 0
loop:
  z = z * @Fun1(@ZCoeff ^ z) + z ^ @Fun2(@Exponent) + #pixel
bailout:
  |z| < @Bailout  
default:
  title = "BWP 33"
  center = (0, 0.1)
  magn = 2
  param ZCoeff
    caption = "Z Coefficient"
    default = (0, 0.3)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 2.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
switch:
  type = "bwp34"
  Seed = #pixel
  ZCoeff = @ZCoeff
  Exponent = @Exponent
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp34 {
init:
  z = #pixel
loop:
  z = z * @Fun1(@ZCoeff ^ z) + z ^ @Fun2(@Exponent) + @seed
bailout:
  |z| < @Bailout  
default:
  title = "BWP 34"
  center = (0, 0.1)
  magn = 2
  param Seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param ZCoeff
    caption = "Z Coefficient"
    default = (0, 0.3)
  endparam
  param Exponent
    caption = "Exponent"
    default = (2, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 2.0
  endparam
  func Fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
switch:
  type = "bwp33"
  ZCoeff = @ZCoeff
  Exponent = @Exponent
  Fun1 = @Fun1
  Fun2 = @Fun2
  Bailout = @Bailout
}

bwp35 {
; z = z ^ e + c
  p = @p2 + PI
  q = 2 * PI * trunc(p / (2 * PI))
  r = @p2 - q
  z = c = #pixel 
loop:
  z = log(z)
  if (imag(z) > r)
    z = z + flip(2 * PI)
  endif
  z = exp(@p1 * (z + flip(q))) + c
bailout:
  |z| < @Bailout  
default:
  title = "BWP 35"
  param p1
    caption = "Parameter 1"
    default = (2, 0)
  endparam
  param p2
    caption = "Parameter 2"
    default = 1
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 2.0
  endparam
}

bwp36 {
init:
  z = @InitValue
  t = #pixel
loop:
  z = @Fun1(z) - @Fun2(t)
  t = @Fun3(z ^ @Exponent)
bailout:
  |z| < @Bailout  
default:
  title = "BWP 36"
  param InitValue
    caption = "Initial Value"
    default = (0, 0)
  endparam
  param Exponent
    caption = "Exponent"
    default = (1, 0)
  endparam
  param Bailout
    caption = "Bailout Value"
    default = 4.0
  endparam
  func Fun1
    caption = "Function 1"
    default = sin()
  endfunc
  func Fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func Fun3
    caption = "Function 3"
    default = recip()
  endfunc
}

bwp37 {
init:
  zc = #pixel
  int n = @exp
  int nm1 = n - 1
loop:
  fp = @fun1(zc) ^ @fun2(nm1)
  f = zc * fp - (1.0, 0.0)
  dz = f / (fp * n)
  zc = zc - dz
  z = 1 / dz
bailout:
  |z| < @bailout
default:
  title="BWP 37"
  maxiter = 100
  periodicity = 0
  center = (0.0, 0.0)
  magn = 1.0
  angle = 0
  param exp
    caption = "Exponent"
    default = 4
    min = 2
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100.0
    min = 0.0
    hint = "make large"
  endparam
  func fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func fun2
    caption = "Function 2"
    default = ident()
  endfunc
}

bwp38 {
init:
  zc = #pixel
  n = @exp
  nm1 = n - 1
loop:
  fp = @fun1(zc) ^ @fun2(nm1)
  f = zc * fp - (1.0, 0.0)
  dz = f / (fp * n)
  zc = zc - dz
  z = 1 / dz
bailout:
  |z| < @bailout
default:
  title="BWP 38"
  maxiter = 100
  periodicity = 0
  center = (0.0, 0.0)
  magn = 1.0
  angle = 0
  param exp
    caption = "Exponent"
    default = (4, 0)
    min = (2, 0)
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100.0
    min = 0.0
    hint = "make large"
  endparam
  func fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func fun2
    caption = "Function 2"
    default = ident()
  endfunc
}

bwp39 {
init:
  zc = #pixel
  n = @exp
  nm1 = n - 1
loop:
  fp = @fun1(zc) ^ @fun2(nm1) + @fun3(#pixel)
  f = zc * fp - (1.0, 0.0)
  dz = f / (fp * n)
  zc = zc - dz
  z = 1 / dz
bailout:
  |z| < @bailout
default:
  title="BWP 39"
  maxiter = 100
  periodicity = 0
  center = (0.0, 0.0)
  magn = 1.0
  angle = 0
  param exp
    caption = "Exponent"
    default = (4, 0)
    min = (2, 0)
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100.0
    min = 0.0
  endparam
  func fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func fun3
    caption = "Function 3"
    default = ident()
  endfunc
}

bwp40 {
init:
  zc = #pixel
  n = @exp
  nm1 = n - 1
  zm = 0
loop:
  zm = zm ^ n + @fun3(#pixel)
  fp = @fun1(zc) ^ @fun2(nm1) + zm
  f = zc * fp - (1.0, 0.0)
  dz = f / (fp * n)
  zc = zc - dz
  z = 1 / dz
bailout:
  |z| < @bailout
default:
  title="BWP 40"
  maxiter = 100
  periodicity = 0
  center = (0.0, 0.0)
  magn = 1.0
  angle = 0
  param exp
    caption = "Exponent"
    default = (4, 0)
    min = (2, 0)
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100.0
    min = 0.0
  endparam
  func fun1
    caption = "Function 1"
    default = ident()
  endfunc
  func fun2
    caption = "Function 2"
    default = ident()
  endfunc
  func fun3
    caption = "Function 3"
    default = ident()
  endfunc
}

bwp41 {
init:
  pix = #pixel
  u = real(pix)
  v = imag(pix)
  a = pi * @a1
  b = pi * @a2
  g = pi * @a3
  d = pi * @a4
  ca = cos(a)
  cb = cos(b)
  sb = sin(b)
  cg = cos(g)
  sg = sin(g)
  cd = cos(d)
  sd = sin(d)
  p = u * cg * cd - v * (ca * sb * sg * cd + ca * cb * sd)
  q = u * cg * sd + v * (ca * cb * cd - ca * sb * sg * sd)
  r = u * sg + v * ca * sb * cg
  s = v * sin(a)
  c = p + flip(q) + @o1
  z = r + flip(s) + @o2
loop:
  z = z ^ @exp + c
bailout:
  |z| <= @bailout
default:
  title="BWP 41"
  param exp
    caption = "Exponent"
default = (2, 0)
  endparam
  param a1
    caption = "Angle 1"
  endparam
  param a2
    caption = "Angle 2"
  endparam
  param a3
    caption = "Angle 3"
  endparam
  param a4
    caption = "Angle 4"
  endparam
  param o1
    caption = "Offset 1"
  endparam
  param o2
    caption = "Offset 2"
  endparam
  param bailout
    caption = "Bailout Value"
    default = 9
  endparam
}

bwp42 {
init:
  z = @init
loop:
  z = 4 * @r * (z ^ @e1) * (1 - (z ^ @e2)) + #pixel
bailout:
  |z| <= @bailout
default:
  title="BWP 42"
  maxiter = 1000
  periodicity = 0
  center = (0, 0)
  magn = 4
  angle = 0
  param init
    caption = "Initial Value"
    default = (0.75, 0.0)
  endparam
  param r
    caption = "R"
    default = (0.75, 0.0)
  endparam
  param e1
    caption = "Exponent 1"
    default = (1, 0)
  endparam
  param e2
    caption = "Exponent 2"
    default = (1, 0)
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100
  endparam
switch:
  type = "bwp43"
  seed = #pixel
  r = @r
  e1 = @e1
  e2 = @e2
  bailout = @bailout
}

bwp43 {
init:
  z = #pixel
loop:
  z = 4 * @r * (z ^ @e1) * (1 - (z ^ @e2)) + @seed
bailout:
  |z| <= @bailout
default:
  title="BWP 43"
  maxiter = 1000
  periodicity = 0
  center = (0.5, 0)
  magn = 4
  angle = 0
  param seed
    caption = "Seed"
    default = (0, 0)
  endparam
  param r
    caption = "R"
    default = (0.75, 0.0)
  endparam
  param e1
    caption = "Exponent 1"
    default = (1, 0)
  endparam
  param e2
    caption = "Exponent 2"
    default = (1, 0)
  endparam
  param bailout
    caption = "Bailout Value"
    default = 100
  endparam
switch:
  type = "bwp42"
  r = @r
  e1 = @e1
  e2 = @e2
  bailout = @bailout
}

bwp44 {
; A generalization of Jim Muth's MandNewt formulas
init:
  z = c = @f1(@p1 * #pixel)
loop:
  a = z ^ @p2 + (c - @p3) * @f2(z) - @f3(@p4 * c)
  b = @p5 * z ^ @p6 + @f4(@p7 * c - @p8)
  z = z - @f5(@p9 * a / b)
bailout:
  |a| >= @bailout
default:
  title="BWP 44"
  method = onepass
  periodicity = 0
  maxiter = 1000
  param p1
    caption = "Parameter 1"
    default = (1, 0)
  endparam
  param p2
    caption = "Parameter 2"
    default = (3, 0)
  endparam
  param p3
    caption = "Parameter 3"
    default = (1, 0)
  endparam
  param p4
    caption = "Parameter 4"
    default = (1, 0)
  endparam
  param p5
    caption = "Parameter 5"
    default = (3, 0)
  endparam
  param p6
    caption = "Parameter 6"
    default = (2, 0)
  endparam
  param p7
    caption = "Parameter 7"
    default = (1, 0)
  endparam
  param p8
    caption = "Parameter 8"
    default = (1, 0)
  endparam
  param p9
    caption = "Parameter 9"
    default = (1, 0)
  endparam
  param bailout
    caption = "Bailout"
    default = (1E-10, 0)
  endparam
  func f1
    caption = "Function 1"
    default = ident()
  endfunc
  func f2
    caption = "Function 2"
    default = ident()
  endfunc
  func f3
    caption = "Function 3"
    default = ident()
  endfunc
  func f4
    caption = "Function 4"
    default = ident()
  endfunc
  func f5
    caption = "Function 5"
    default = ident()
  endfunc
}