Sign in

ponder technology

@ponder.technology
51 followers 1 following 1 posts

independent multidisciplinary research laboratory expanding the horizons of mathematics, art, philosophy, and computing contact: research@ponder.technology

PostsRepliesMedia
ponder technology @ponder.technology · 04/09/2026
Ponder Technology has no affiliation with the Fluoddity project but if you like the sort of research we do here you'll love Fluoddity! It's an artificial life system, a more generalized approach to "physarum"-style simulations, with an incredibly rich space of behaviors. A highly recommended follow.
1171
Reposted by ponder technology
ponder @ponder.ooo · 19/06/2026
this means the idea of gluing together the lyapunov exponent manifolds of all the unique offsets of the forcing sequence of the logistic map with periodic forcing is back on the table!! we can indeed create the self-intersecting offset-agnostic lyapunov sheet for each sequence
AB fractalABB fractalABBAB fractal
071
Reposted by ponder technology
ponder @ponder.ooo · 19/06/2026
not particularly shocking but easier to see in 3d that every "branch" or "antenna" of the figures that appear in the lyapunov fractal is basically just the plain logistic map's lyapunov exponent graph "swept out" across a curve
cross section of a 3d render of a lyapunov fractalanother one, multiple branches of different colors overlappinganother onesomebody's graph of the logistic map's lyapunov exponent
151
Reposted by ponder technology
ponder @ponder.ooo · 28/12/2025
at n=6 it's back to two curves (3 if you count the real line), and n=7 back to 1; plane separated into 4n+2 regions the shit going on *inside* those regions stays messy as hell past n=5 ofc but at least the decomposition of the plane into ≤3 types of fundamental region seems to hold for c=(1-1/n)
n=6
13 regions in the upper half-plane, so 26 total, decomposing to 2+6+6n=7, single curve w/ 7*3 self-intersections, + the real line, dividing the plane into 30 regions, only the upper half ones are numbered in the image
121
Reposted by ponder technology
ponder @ponder.ooo · 28/12/2025
r exp(i * theta) -> (r + cos(theta))exp(i * theta) - c c=(1-1/n), n in {2,3,4,5}
c=2
not a super complicated patternc=3
a bit more structure, still not super complicatedc=4
still pretty simple structurec=5
much more complexity, both in the overall structure and the finer details
182
Reposted by ponder technology
ponder @ponder.ooo · 28/12/2025
adding or subtracting a small epsilon from c=(4/5) leads to a dramatic shift so even tho the c=(1-1/n) pattern gets markedly weirder at n=5, it is still doing something very different from arbitrary values of c
c=0.7998c=0.8001
1122
Reposted by ponder technology
ponder @ponder.ooo · 29/07/2025
tracking orbits of the projective shift map; green line shows the trajectory of a particular pointanother trajectoryand anotherand another
111
Reposted by ponder technology
ponder @ponder.ooo · 29/05/2026
stochasticity vs true average; also min and max across offsets, which are definitely WP:OR and probably will never exist in a wikipedia-referenceable source 😔
stochasticaverageminmax
031
Reposted by ponder technology
ponder @ponder.ooo · 02/08/2026
4181
Reposted by ponder technology
ponder @ponder.ooo · 09/08/2026
higher-fidelity version of what kimi was cooking
orbit densities of a chaotic mapsame, but viewed from another angle
0252
Reposted by ponder technology
ponder @ponder.ooo · 09/08/2026
3483
Reposted by ponder technology
ponder @ponder.ooo · 10/08/2026
071
Reposted by ponder technology
ponder @ponder.ooo · 22/08/2026
similar rendersfibrous textures
1322
Reposted by ponder technology
ponder @ponder.ooo · 24/08/2026
math thing
2122
Reposted by ponder technology
ponder @ponder.ooo · 24/08/2026
finally tested the idea of alternating between multiple shift values and indeed there is a more general class of patterns to be found
strange patterns. reminiscent of the ones i have posted before but not quite the same
062
Reposted by ponder technology
ponder @ponder.ooo · 26/08/2026
creature
2181
Reposted by ponder technology
ponder @ponder.ooo · 16/03/2026
hyperparam fractal a la arxiv.org/abs/2402.06184 steepest g.d. (left) vs adamw (right), all other settings identical main takeaway: noted in the original paper is that the region of best convergence (pale teal) is pressed right up against the boundary of convergence; w/ adamw this is not the case
sgd versionadamw version
131
Reposted by ponder technology
ponder @ponder.ooo · 01/09/2026
a new optimizer has entered the ring. meet the muon blob
muon blob
021
Reposted by ponder technology
ponder @ponder.ooo · 01/09/2026
2104
Reposted by ponder technology
ponder @ponder.ooo · 02/09/2026
currently just generating these randomly but what they are is basically functions, non-injective to varying degrees, from nodes of a quadtree to 2d vectors (quantized to lattice points). would be easy to make properly injective mappings but there's a tradeoff btwn that & how much resolution you need
more weird lattice diagrams
284