1 - Output Types
1.1 - domain
Generic output for domain colourings.
- Size/quality can be changed with bmp width and height.
- Alternative generator methods: generategif, generatemapping, and generate inverse are also under this.
1.2 - graphing
Graphs the function in 2D.
- Red = real part, Blue = imaginary part.
- start locations and end location define a line in the complex domain.
- maximum parameter:
- Positive → sets the maximum height of the graph.
- 0 → automatically sets maximum.
- Negative → directly sets the max output range (positive values take maximum value, and maximum’s minimum).
1.2.1 - polar graph
Checkbox at the right makes it a polar graph.
- Moving along a contour: imaginary parts set y-axis, real part sets real axis.
- To make parametric: use f(x)+i*g(x).
1.3 - numerical
Input the number for substituting x → get result.
1.4 - heightmap
- Use capslock ON for movement:
- WASDZX → move (Z/X = up/down, W/S = forward/backward).
- QE, CV, RF → rotate.
- Click reset camera to reset movement.
1.4.0.1
T (capital) changes heightmap from magnitude → real part → imaginary part (cycles every 3).
1.4.1
maximum height parameter:
- Set to 0 → height always = 1.
1.4.2
download stl → downloads mesh as STL.
⚠ Mesh might be large or have NaN values, loading STLs may be slow.
1.4.3
download objects → downloads as .gltf (Three.js format).
1.4.4 - create gif
Creates a GIF rotating around the mesh. Options:
1. default - circular path looking down (sqrt2).
2. close - smaller orbit (1).
3. ortho - camera orbits flat plane (z=0), no tilt.
4. zero - camera at origin, spins in place.
5. zeroup - camera at origin, spins while angled up.
6. topdown - rotates around Z-axis, looking down.
7. flyover - camera moves in a straight line past origin.
8. spherical - 45° up view, circle path (z=0, r=0.9).
1.4.5
Buttons at bottom left change the mesh directly (not the camera) — useful for GIFs.
2 - Image Generation
2.0
Variables:
- x, z can be used.
- q → nome inputs.
- t → period ratio τ.
- modulartransformqt = div(log(q), I, pi())
- modulartransformtq(t) = exp(mul(pi(), I, t))
- Note: t cannot be used when making GIFs.
2.1 - generate
Generates domain coloring on the domain canvas.
2.2 - generate inverse
Colors as initial point and draws at output complex number (inverse).
- Faster than newtoninv('sin(x)', x) but you cannot get values.
2.3 - generate mapping
For conformal maps (e.g., Schwarz triangle function).
- Similar to generate inverse, but only draws gridlines.
2.4 - generate gifs
Uses variable t moving from 0 to 1.
- Suggestion: use sin(pi*t) for easing.
- Cannot use t for period ratio when doing this.
2.5 - mesh generation
Under toggle mesh:
- Heightmap generated from magnitude of output.
- Use maximum height in heightmap area to limit height.
2.5.1 - create mesh
Creates heightmap.
2.5.2 - create spherical mesh
Uses spherical coordinates (θ, φ).
- F(θ, φ) = f(θ + φ*i).
- Should have periods 2π in both real and imaginary axis.
2.5.3 - create stereographic mesh
For functions such as stereopcube (stereographic projection).
2.5.4 - create toroidal mesh
- Function should have period 1 in both imaginary and real axes.
- For functions like cm, use unwarp(x, w1, w2) where w1, w2 are periods.
- Example: cm(unwarp(5*x, 5.29991625, exp(2*pi*i/3)*5.29991625)).
2.5.5 - cylindric mesh
- Function should be periodic along the real axis with period 1.
3 - Color Modes
3.1 - contour
Draws lines where f(x) components get close to an integer.
3.1.2 - pcontour
Polar contour (uses arg & mag instead of re & im).
3.1.3 - acountour
Antialias contour (slow, minimal advantages).
3.2 - HSV
Value from magnitude-to-lightness function plus other methods below.
3.3 - HSL
3.4 - HCL
3.5 - LCH
Cylindrical version of CIELAB color space.
3.6 - YCbCr
Real part → blue, Imag part → red.
3.7 - YDbDr
Same as YCbCr.
3.8 - YCoCg
Real part → orange, Imag part → green.
3.9 - YPbPr
Blue and red again.
3.10 - real
Colors based on real part of output.
3.11 - image
Colors based on imaginary part.
3.12 - 2d
Technical; used to save function for use in other software.
3.13 - palette
User can choose palette by loading 360×100 BMP or selecting colors.
3.14 - freeRGB
[r, g, b] from magnitude-to-lightness. Example:
[mag(x), sqr(x), log(1+re(x)^2)]
3.15 - freeHSV
[h, s, v]. Example:
[360+arg(z)/pi*180, 100, log(x+1)*100]
3.16 - freeHSL
[h, s, l]. Example:
[360+arg(z)/pi*180, 100, (x+1)/x*100]
3.17 - isolines
Draws lines of equal magnitude.
3.18 - dynamic
Changes with time (good for GIFs).
3.19 - magnitudeold (Magnitude 2)
Colors by magnitude.
3.20 - magnitude (Magnitude)
Colors by magnitude.
3.21 - magnitudecolour (Magnitude 3)
Colors by magnitude.
3.22 - magnitude4 (Magnitude 4)
Colors by magnitude.
3.23 - neon
Brighter where f(x) components get close to an integer.
3.24 - differ
Based on difference between means of real and imaginary parts.
3.25 - purify
"Cool" effect.
3.26 - quadrant
Colors depending only on angle — colors quadrants.
3.27 - upperplanebw
Imag > 0 → white, else black.
3.28 - unitcirclebw
Inside unit circle → white, else black.
3.29 - trisect
Similar to quadrant but 3 colors.
3.30 - hexasect
Similar to quadrant but 6 colors.
3.31 - octant
Similar to quadrant but 8 colors.
3.32 - dodecant
Similar to quadrant but 12 colors.
3.33 - griddistort
Checkerboard (smooth).
3.34 - griddistorts
Checkerboard (unsmooth).
3.35 - griddistortbw
Checkerboard (black and white).
3.36 - realimagheat
Colors based on imag^2/real and real^2/imag.