In Newton's and Einstein's theory, all mass gravitates in an isotropic (spherical) manner. In this paper, we will consider ellipsoidal -- anisotropic -- gravitating processes. We discuss dark matter, as well as dark energy and the possibility of a final, 5th interaction.

A simple numerical solution for general relativity in the Newtonian weak field regime is provided -- no tensor calculus is required. The topics under consideration are the deflection of photons and neutrinos by the Sun, the relativistic rotation of Mercury's orbit plane, the Shapiro time delay, and the gravitational redshift -- namely, the four Solar System tests of general relativity. To simplify the calculations, Euler integration is used. Hopefully, this numerical solution can be found to be an important tool, primarily due to this simplicity.

In Newton’s theory, all mass gravitates in an isotropic (spherical) manner. In this paper, we will consider aspherical – anisotropic – gravitating processes, which leads to a unique view of dark matter: dark matter is a graviton condensate. We also discuss dark energy, and the possibility of a final, 5th interaction. This paper discusses some physical phenomena, including the effects of dark matter and dark energy. A unified table of interactions is given.

By quantizing the kinematic and gravitational time dilation using various step sizes, one obtains a set of weighted orbit paths. The precession associated with each weighted orbit path combines to provide the same answer as the classical analytical solution.

In this paper we introduce a natural method for producing both refraction and reflection caustics in backward path tracing (e.g. bouncing around an eye ray in the scene until a light is found). These caustics do not rely on a light location, and as such, do not rely on bidirectional or forward path tracing. As such, these caustics allow for as many light sources as one would care for; the shapes and positions of the lights are completely arbitrary (can be bunny shaped, etc). We use the standard Cornell box for testing the backward path tracer.

In a previous paper, we introduced a model that accounts for both dark matter and dark energy. In this paper we will attempt to refute objections to the model.

With regard to the separating isosurface of two classes of objects in two-dimensional space, the transition from rectilinear to curvilinear is documented. Marching Squares and OpenCV were used to calculate the data that were used for illustrations in this paper. It is found that the curvilinearity is adjustable via variable grid resolution, as well as via convolution such as Gaussian blur. This paper's reference section is rather small, and the hunt for the literature is left to those who have access to the journals.

The theme of this research is an examination of the traditional multiplication operator, in the case of fractal sets in $n \geq 1$ embedding dimensions. After this examination, an alternative, new multiplication operator is introduced. The traditional multiplication operator has a time complexity of $O(n^2)$, whereas the new multiplication operator has a time complexity of $O(n)$. Taking amortized costs into account, it is found that the new multiplication operator is more time-efficient where $n \geq 32$, using an optimizing C++ compiler. There is no problem, other than concerns about time complexity, with the traditional multiplication operator. It was hypothesized that there would be differences between the two multiplication operators. These differences, and some similarities, between the two multiplication operators are visualized in terms of fractal sets, via OpenGL. The C++ and Python code is available upon request.