Computational art — fractals, physics visualizations, and generative geometry by a recreational physicist.https://curvatureofthemind.com/https://curvatureofthemind.com/posts/what-a-function-does-to-a-space-of-functions/https://curvatureofthemind.com/posts/what-a-function-does-to-a-space-of-functions/A polynomial is a point in a vector space. Shifting, scaling, differentiating, and substituting are maps of that space into itself, and the only question worth asking about any of them is what happens to the degree.Sat, 11 Jul 2026 11:00:00 GMTExperimentshttps://curvatureofthemind.com/posts/five-ways-to-draw-the-same-fractal/https://curvatureofthemind.com/posts/five-ways-to-draw-the-same-fractal/The fractal designer now carries five renderers, an aspect-aware workspace, and a button that hands you a clean PNG. Three of the five were quietly drawing the wrong thing.Thu, 09 Jul 2026 09:00:00 GMTExperimentshttps://curvatureofthemind.com/posts/the-logistic-equation-on-a-line/https://curvatureofthemind.com/posts/the-logistic-equation-on-a-line/A single population grows without bound, predators can only cage it into a boom-and-bust cycle, and the honest fix is a population that limits itself: the S-curve.Mon, 06 Jul 2026 11:00:00 GMTPhysicshttps://curvatureofthemind.com/posts/van-der-pol-and-the-birth-of-a-limit-cycle/https://curvatureofthemind.com/posts/van-der-pol-and-the-birth-of-a-limit-cycle/An oscillator with friction that changes its mind. Small swings get pumped up, big ones get bled down, and everything meets on a single closed loop the whole plane falls onto.Mon, 06 Jul 2026 10:30:00 GMTPhysicshttps://curvatureofthemind.com/posts/the-pendulum-the-cats-eye-and-a-little-friction/https://curvatureofthemind.com/posts/the-pendulum-the-cats-eye-and-a-little-friction/The pendulum is the spring with the small-angle lie removed. Putting the full sine back in bends its phase space into the cat's-eye pattern, and friction drains it.Mon, 06 Jul 2026 10:00:00 GMTPhysicshttps://curvatureofthemind.com/posts/the-spring-equation-and-the-shape-of-simple-motion/https://curvatureofthemind.com/posts/the-spring-equation-and-the-shape-of-simple-motion/Where the spring equation comes from, and why its phase space is a family of nested ellipses that damping turns into a spiral.Mon, 06 Jul 2026 09:30:00 GMTPhysicshttps://curvatureofthemind.com/posts/drawing-differential-equations-as-wind/https://curvatureofthemind.com/posts/drawing-differential-equations-as-wind/An old widget of mine, rebuilt in plain javascript, that draws the phase space of a differential equation the way those wind maps draw the wind.Mon, 06 Jul 2026 09:00:00 GMTPhysicsExperimentshttps://curvatureofthemind.com/posts/evil-cauliflower/https://curvatureofthemind.com/posts/evil-cauliflower/Tue, 25 Nov 2014 14:38:52 GMTImageshttps://curvatureofthemind.com/posts/clearing-stuff/https://curvatureofthemind.com/posts/clearing-stuff/Sun, 09 Nov 2014 12:48:05 GMTImageshttps://curvatureofthemind.com/posts/new-feature-download-demo-image/https://curvatureofthemind.com/posts/new-feature-download-demo-image/Thu, 28 Nov 2013 00:04:58 GMTExperimentsImageshttps://curvatureofthemind.com/posts/symmetric-almost/https://curvatureofthemind.com/posts/symmetric-almost/Sat, 21 Sep 2013 19:30:34 GMTImageshttps://curvatureofthemind.com/posts/hexagonal-snowflake/https://curvatureofthemind.com/posts/hexagonal-snowflake/Mon, 17 Jun 2013 11:16:29 GMTImageshttps://curvatureofthemind.com/posts/718/https://curvatureofthemind.com/posts/718/Fri, 14 Jun 2013 11:01:57 GMTImageshttps://curvatureofthemind.com/posts/replicated-triangles/https://curvatureofthemind.com/posts/replicated-triangles/Wed, 12 Jun 2013 00:24:56 GMTImageshttps://curvatureofthemind.com/posts/713/https://curvatureofthemind.com/posts/713/Tue, 11 Jun 2013 00:21:21 GMTImageshttps://curvatureofthemind.com/posts/fractal-grid2/https://curvatureofthemind.com/posts/fractal-grid2/Thu, 06 Jun 2013 06:08:48 GMTImageshttps://curvatureofthemind.com/posts/fractal-ruler/https://curvatureofthemind.com/posts/fractal-ruler/Wed, 05 Jun 2013 13:08:27 GMTImageshttps://curvatureofthemind.com/posts/grid-deconstructed/https://curvatureofthemind.com/posts/grid-deconstructed/Fri, 22 Mar 2013 10:22:50 GMTImageshttps://curvatureofthemind.com/posts/another-image-busy-busy/https://curvatureofthemind.com/posts/another-image-busy-busy/Sun, 17 Mar 2013 23:06:32 GMTImageshttps://curvatureofthemind.com/posts/fractal-friday-wisp/https://curvatureofthemind.com/posts/fractal-friday-wisp/Fri, 08 Mar 2013 10:00:00 GMTImageshttps://curvatureofthemind.com/posts/fractal-friday-alignment/https://curvatureofthemind.com/posts/fractal-friday-alignment/Fri, 01 Mar 2013 10:00:00 GMTImageshttps://curvatureofthemind.com/posts/fractal-friday-darkness/https://curvatureofthemind.com/posts/fractal-friday-darkness/Fri, 22 Feb 2013 10:00:00 GMTImageshttps://curvatureofthemind.com/posts/more-crossing-lines-images/https://curvatureofthemind.com/posts/more-crossing-lines-images/Wed, 20 Feb 2013 13:21:29 GMTExperimentshttps://curvatureofthemind.com/posts/fractal-friday/https://curvatureofthemind.com/posts/fractal-friday/Fri, 15 Feb 2013 10:00:00 GMTImageshttps://curvatureofthemind.com/posts/playing-around-with-overlapping-lines/https://curvatureofthemind.com/posts/playing-around-with-overlapping-lines/Wed, 13 Feb 2013 12:50:32 GMTImageshttps://curvatureofthemind.com/posts/some-simple-geometric-fractals/https://curvatureofthemind.com/posts/some-simple-geometric-fractals/Sat, 09 Feb 2013 22:30:58 GMTImageshttps://curvatureofthemind.com/posts/just-post-something-jeeezz/https://curvatureofthemind.com/posts/just-post-something-jeeezz/Sat, 26 Jan 2013 23:01:57 GMTImageshttps://curvatureofthemind.com/posts/varying-circle-grid-and-color/https://curvatureofthemind.com/posts/varying-circle-grid-and-color/Fri, 11 Jan 2013 14:02:46 GMTExperimentsImageshttps://curvatureofthemind.com/posts/grid-of-overlapping-circles/https://curvatureofthemind.com/posts/grid-of-overlapping-circles/Thu, 10 Jan 2013 14:00:28 GMTImageshttps://curvatureofthemind.com/posts/a-bunch-of-circles/https://curvatureofthemind.com/posts/a-bunch-of-circles/Wed, 09 Jan 2013 23:00:05 GMTImages