Mystic Amused @Mysticamused@gamemaking.social

Experiments with multiplying the Z-coordinates of a sphere. The distortion effect is being applied to the final view, not the object itself, simulating the barrel distortion one might see on a wide angle lens.

#barreldistortion, #sphere, #lens, #math, #excel

I've been experimenting with cellular automata. The differences of powers of 8 is one of my favorite patterns so far. I imagined the skin of the grim reaper to resemble this, a tapestry of infinitely expanding living patterns, and the triangular voids representing their recurrent ends.

#cellularautomata, #sierpinski, #triangle, #fractal, #generativeart

3D screw-spirals, 3/4 and front views. I'm facinated by how these resemble living creatures. Could even more complex life forms have their topology simplified down to mathematical oscillations?

Circle One ( Cos(a)*(1-(c*.003)^2), Sin(a)*(1-(c*.003)^2) )
Circle Two ( Sin(b)*(1-(c*.003)^2), Cos(a)*(1-(c*.003)^2) )
Element (0, 0, n)

Screw-Spiral (Cos(a)*(1-(c*.003)^2) + Sin(b)*(1-(c*.003)^2), Sin(a)*(1-(c*.003)^2) + Cos(a)*(1-(c*.003)^2) + n)

#3d, #spiral, #oscillation, #math, #topology

My favorite curve graphs resemble the phi double spiral, not unlike the pattern found in sunflowers or pine cones. These graphs are drawn from a point on the edge, inside of, or outside of a circle rolling centered on the edge of another circle. Various increments for a & b.

Circle One (Cos(a), Sin(a))
Circle Two (Sin(b), Cos(b))

Spiral (Cos(a)+Sin(b), Sin(a)+Cos(b))

#curve, #roulette, #sunflower, #phidoublespiral, #math

Using VBA in Excel I've been able to generate vertex coordinates, line series, graphs and rotational matrices for hypercubes of any dimension. The key to "connecting the dots" is to search for vertices whose coordinates match for all but one value.

#hypercube, #cube, #tesseract, #penteract, #math

Experimented with sphere flattening by multiplying up the Z coordinate.

Each circle created using cosine & sine for x, y. Longitude created from a series of 18 circles rotated in 10 degree increments about the y-axis. Latitude created from circles evenly spaced about the y-axis and sized by using the height as the amplitude for the trig functions, i.e. multiplying the cosine and sine by the square root of 1 minus the y-position squared.

#sphere, #polar, #wireframe, #math, #excel

Using Excel, I learned how to generate the Sierpinski triangle fractal using differences of powers of 2. Column A is a number line with absolute values. Column B is composed of the previous numbers squared. Column C and onward are the adjacent differences.

#sierpinski, #triangle, #fractal, #excel, #math