XIII
Showing posts tagged math
The Fourier transform takes an input function f (in red) in the “time domain” and converts it into a new function f-hat (in blue) in the “frequency domain”.
In other words, the original function can be thought of as being “amplitude given time”, and the Fourier transform of the function is “amplitude given frequency”.
Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph. In practice, these peaks are never that sharp. That would require infinite precision.
I’m not too happy with this one yet. It’s a bit of a mixture of Fourier series and Fourier transform. The animation could also be a bit smoother in some steps. I may tweak it later.
Spiral of equilateral triangles with side lengths which follow the Padovan sequence.
Graphs of six convex regular 4-polytopes
In geometry, a polychoron or 4-polytope is a four-dimensional polytope.[1][2] It is a connected and closed figure, composed of lower dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells.
The two-dimensional analogue of a polychoron is a polygon, and the three-dimensional analogue is a polyhedron. The term polychoron (plural polychora), from the Greek roots poly (‘many’) and choros (‘room’ or ‘space’) and has been advocated by Norman Johnson and George Olshevsky, but it is little known in general polytope theory. Other names for polychoron include: polyhedroid and polycell.
Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space.
Phase Patterns: Autechre’s Gantz Graf
geometric systems are most important
Stanley Kubrick and The Saturn Death Cult
“Is the greater body of Stanley Kubrick’s films an exposé of a hidden elite obsessed with dark Saturnian sexual rites, paedophilia and the planned ritualistic transmutation of mankind?”
2001: A Space Odyssey: Kubrick’s undoubted masterpiece and at the centre of Jay Weidner’s alchemical take on Kubrick’s films. As discussed above, Weidner claims this film to be Kubrick’s attempt at an initiation rite of passage illustrating humanity’s next planned-for evolutionary step. Weidner believes Kubrick has revealed an occult agenda to launch us as a species into space where we will be able to embrace our destiny as future star children and join the greater cosmos.
Necropolis at Meroe
Pyramid of Cestius - Giovanni Battista Piranesi
