|
#rand |
Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
|
|
Complex |
|
#random |
Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
|
|
Complex |
|
@fn1 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
@fn2 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
@fn3 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
@fn4 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
abs |
The absolute value of a number. abs(3) = abs(-3) = 3.
abs() of a complex number is a complex number consisting of
the absolute values of the real and imaginary parts, i.e.
abs(a,b) = (abs(a),abs(b)).
|
Int
|
Int |
|
Float
|
Float |
|
Complex
|
Complex |
|
acos |
Inverse cosine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
acosh |
Inverse hyperbolic cosine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
alpha |
The alpha component of a color. Can be assigned to.
|
Color
|
Float |
|
asin |
Inverse sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
asinh |
Inverse hyperbolic sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
atan |
Inverse tangent function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
atan2 |
The angle between this complex number and the real line,
aka the complex argument.
|
Complex
|
Float |
|
atanh |
Inverse hyperbolic tangent function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
blend |
Blend two colors together in the ratio given by the 3rd parameter.
|
Color, Color, Float
|
Color |
|
blue |
The blue component of a color. Can be assigned to.
|
Color
|
Float |
|
bool |
Construct a boolean. It's not really required (bool x = bool(true) is just the same as bool x = true) but is included for consistency.
|
Bool
|
Bool |
|
cabs |
The complex modulus of a complex number z.
cabs(a,b) is equivalent to sqrt(a*a+b*b).
This is also the same as sqrt(|z|)
|
Complex
|
Float |
|
ceil |
Round up to the next highest number.
|
Float
|
Int |
|
Complex
|
Complex |
|
cmag |
The squared modulus of a complex or hypercomplex number z.
cmag(a,b) is equivalent to a*a+b*b. This is the same as |z|.
|
Complex
|
Float |
|
Hyper
|
Float |
|
color |
Constructs a new color from floating point red, green, blue and alpha
components. Equivalent to rgba.
|
Float, Float, Float, Float
|
Color |
|
complex |
Construct a complex number from two real parts.
complex(a,b) is equivalent to (a,b).
|
Float, Float
|
Complex |
|
compose |
Composite the second color on top of the first, with opacity given
by the 3rd parameter.
|
Color, Color, Float
|
Color |
|
conj |
The complex conjugate. conj(a,b) is equivalent to (a,-b).
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
cos |
trigonometric sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
cosh |
Hyperbolic cosine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
cosxx |
Incorrect version of cosine function. Provided for backwards
compatibility with equivalent wrong function in Fractint.
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
cotan |
Trigonometric cotangent function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
cotanh |
Hyperbolic cotangent function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
exp |
exp(x) is equivalent to e^x
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
flip |
Swap the real and imaginary parts of a complex number.
flip(a,b) = (b,a).
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
float |
Construct a floating-point number.
|
Float
|
Float |
|
floor |
Round down to the next lowest number.
|
Float
|
Int |
|
Complex
|
Complex |
|
fn1 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
fn2 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
fn3 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
fn4 |
Predefined function parameter used by Fractint formulas
|
Complex
|
Complex |
|
gradient |
Look up a color from the default gradient.
|
Float
|
Color |
|
green |
The green component of a color. Can be assigned to.
|
Color
|
Float |
|
hsl |
Create a color from hue, saturation and lightness components. The alpha channel is set to to 1.0 (=100%).
|
Float, Float, Float
|
Color |
|
hsla |
Create a color from hue, saturation and lightness components and an alpha channel.
|
Float, Float, Float, Float
|
Color |
|
hsv |
Create a color from hue, saturation and value components. HSV is a similar color model to HSL but has a different valid range for brightness.
|
Float, Float, Float
|
Color |
|
hue |
The hue of a color.
|
Color
|
Float |
|
hyper |
Construct a hypercomplex number with a real and 3 imaginary parts.
Can be passed either 2 complex numbers or 4 floating-point numbers.
hyper(a,b,c,d) is equivalent to the shorthand (a,b,c,d).
|
Float, Float, Float, Float
|
Hyper |
|
Complex, Complex
|
Hyper |
|
hyper_j |
The 3rd component of a hypercomplex number. Can be assigned to.
hyper_j(a,b,c,d) = c.
|
Hyper
|
Float |
|
hyper_jk |
The 3rd and 4th parts of a hypercomplex number.
Can be assigned to. hyper_jk(a,b,c,d) = (c,d).
|
Hyper
|
Complex |
|
hyper_k |
The 4th component of a hypercomplex number. Can be assigned to.
hyper_k(a,b,c,d) = d.
|
Hyper
|
Float |
|
hyper_ri |
The real and imaginary parts of a hypercomplex number.
Can be assigned to. hyper_ri(a,b,c,d) = (a,b).
|
Hyper
|
Complex |
|
ident |
Do nothing. ident(x) is equivalent to x.
This function is useless in normal formulas but
comes in useful as a value for a function parameter
to a formula. For example, a general formula like z = @fn1(z*z)+c
can be set back to a plain Mandelbrot by setting fn1 to ident.
Note: ident() is compiled out so there's no speed penalty involved.
|
Int
|
Int |
|
Float
|
Float |
|
Complex
|
Complex |
|
Bool
|
Bool |
|
Hyper
|
Hyper |
|
imag |
Extract the imaginary part of a complex or hypercomplex number.
imag(a,b) = b.
imag() is unusual in that it can be assigned to: imag(z) = 7 changes
the imag part of z.
|
Complex
|
Float |
|
Hyper
|
Float |
|
imag2 |
The square of the imaginary part of a complex number.
real2(a,b) = b*b.
While not a generally useful function, this is provided to ease porting
of files from older Gnofract 4D versions.
|
Complex
|
Float |
|
int |
Construct an integer. To convert a float to an int, use floor, ceil, round or trunc instead.
|
Int
|
Int |
|
log |
The natural log.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
lum |
The luminance (or brightness) of a color.
|
Color
|
Float |
|
manhattan |
The Manhattan distance between the origin and complex number z.
manhattan(a,b) is equivalent to abs(a) + abs(b).
|
Complex
|
Float |
|
manhattanish |
A variant on Manhattan distance provided for backwards
compatibility. manhattanish(a,b) is equivalent to a+b.
|
Complex
|
Float |
|
manhattanish2 |
A variant on Manhattan distance provided for backwards
compatibility. manhattanish2(a,b) is equivalent to (a*a + b*b)^2.
|
Complex
|
Float |
|
max |
Returns the larger of its two arguments.
|
Float, Float
|
Float |
|
max2 |
max2(a,b) returns the larger of a*a or b*b. Provided for
backwards compatibility.
|
Complex
|
Float |
|
mergemultiply |
Multiplies colors together. Result is always darker than either input.
|
Color, Color
|
Color |
|
mergenormal |
Returns second color, ignoring first.
|
Color, Color
|
Color |
|
min |
Returns the smaller of its two arguments.
|
Float, Float
|
Float |
|
min2 |
min2(a,b) returns the smaller of a*a or b*b. Provided for
backwards compatibility.
|
Complex
|
Float |
|
neg |
No documentation yet.
|
Int
|
Int |
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
rand |
Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
|
|
Complex |
|
real |
Extract the real part of a complex or hypercomplex number.
real(a,b) = a.
real() is unusual in that it can be assigned to: real(z) = 7 changes
the real part of z.
|
Complex
|
Float |
|
Hyper
|
Float |
|
real2 |
The square of the real part of a complex number.
real2(a,b) = a*a.
While not a generally useful function, this is provided to ease porting
of files from older Gnofract 4D versions.
|
Complex
|
Float |
|
recip |
The reciprocal of a number. recip(x) is equivalent to 1/x.
Note that not all hypercomplex numbers have a proper reciprocal.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
red |
The red component of a color. Can be assigned to.
|
Color
|
Float |
|
rgb |
Create a color from three color components. The alpha channel is set to to 1.0 (=100%).
|
Float, Float, Float
|
Color |
|
rgba |
Create a color from three color components and an alpha channel.
|
Float, Float, Float, Float
|
Color |
|
round |
Round to the nearest number (0.5 rounds up).
|
Float
|
Int |
|
Complex
|
Complex |
|
sat |
The saturation of a color.
|
Color
|
Float |
|
sin |
trigonometric sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
sinh |
Hyperbolic sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
sqr |
Square the argument. sqr(x) is equivalent to x*x or x^2.
|
Int
|
Int |
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
sqrt |
The square root.
The square root of a negative float number is NaN
(ie it is NOT converted to complex). Thus sqrt((-3,0)) != sqrt(-3).
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
tan |
trigonometric sine function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
tanh |
Hyperbolic tangent function.
|
Float
|
Float |
|
Complex
|
Complex |
|
Hyper
|
Hyper |
|
trunc |
Round towards zero.
|
Float
|
Int |
|
Complex
|
Complex |
|
zero |
Returns zero.
|
Int
|
Int |
|
Float
|
Float |
|
Complex
|
Complex |