3D Surface graphing - with mapping, bumps, or textures

Bumps | Patterned texture | Distance haze |
---|---|---|

, | ||

In the Equation Editor as: Y = exp(sin(x) * cos(z)) | In the Equation Editor as: Y = 3 * cos(sin(x) * z)) | In the Equation Editor as: Y = Exp(Sin(x*z))/2 |

With 4DLab, complex surface graphing is meaningful!

The transcomplex Quadratic function | The transcomplex Quartic function | The transcomplex Exponential function |
---|---|---|

In the Equation Editor as: U(x, z) = x ^{2} - z^{2}V(x, z) = 2xz | In the Equation Editor as: U(x, z) = x ^{4} - 6x^{2}z^{2} + z^{4}V(x, z) = 4x ^{3}z - 4xz^{3} | In the Equation Editor as: U(x, z) = Exp(x) * Cos(z), V(x, z) = Exp(x) * Sin(z) |

**4DLab** plots complex functions in an integrated way: the domain and the range of a function are not shown apart. In fact, complex functions are plotted analogously as the real functions are plotted.

The traditional graphing procedure —in textbooks and in other plotting software— is to separate the function domain from the function range; this is because the domain is usually a plane region of a plane, and the range is usually a surface. But **4DLab** follows the new transcomplex numbers approach, where the complex numbers are extended to 4–dimensional ordered pairs.

The transcomplex numbers system is an extension of the complex numbers system to 4 dimensions. Complex variables are 2–dimensional while transcomplexs are 4–dimensional. There are other four entries numbers systems, like, for example, the quaternions. But only the transcomplexs combine the simplicity of the real numbers with the power of the complex numbers. But where the transcomplexs shine above all the others is in the graphs it produces: visually simple and beautiful; no more abstract "surfaces", no more dual and disintegrated plotting. **4DLab** is the software made specially to plot transcomplex surfaces, but since mathematics is an integrated and unified field, **4DLab** also follows this model. Thus, in the same way that 3–dimensional surfaces are plotted, the 2–dimensional real functions are also plotted: you use the same equation editor. Just write-in —the editor will check your syntax— and choose the type of rendering you wish.

**4DLab** was also a program made to produce aesthetically appealing images. There are many choices and parameters to choose or change. So, if you wish, your plots can be done over an appealing background, you can add your name, or the equation involved, etc.

**4DLab** is a new tool for learning math and a new tool for graphing 3D equations and 2D equations. This free software is a3D and 2D graphing software. Choose a picture —any picture; a texture, a landscape, a photograph— and plot it against a surface and you will visually grasp the concept of one-to-one (1–1) mapping. Complex math can be made simple by bringing some abstract concepts down to the point that it becomes personal.

- Surfaces can be shown in grid-only mode, or opaque with or without showing the grid mesh. Axes are shown exactly where they belong: intersecting the surface at the exact points.
- For any function, the domain-to-range relation can be seen instantly by just moving the mouse over the the domain region. The corresponding point of a domain can be seen as a moving point, or as a line connecting the domain with the range. This is an useful tool, especially when a point in the space is relate to another point in the space far away, or not directly above, as with real functions plots.
- The program incorporates a dedicated calculator to compute the coordinates of any point coordinates for any equation set, be them part of the equation domain or not.
- The program can maintain a list of your favorite website links with editable comments. You can click on any of the saved links for immediate reference.
- Decorate any of your math pictures with any background of your preference.
- The coordinates axes names can be changed to adapt to your needs. So, instead of
**X**,**Y**, or**Z**, the axes labels can be named:**Ohms**, or**Degrees**, or**Distance**, etc. - Surface or line pictures can be labeled as
**Fig.1**,**Fig. 2**, etc, or the user can insert, his/her name or a copyright notice. Other labels are available. The notes are saved as part of the pictures. - Surfaces or line plots can be rotated and viewed from any angle. The program can show the surface plots intersection with the
**XY**, or**iZY**planes. Pictures can be resized manually with the mouse, or can be resized exactly to any desired dimension with pixel precision. - The center of coordinates can be moved away from the center of the picture frame for better composition of those offset plots.