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Tim Hutton
Приєднався 6 жов 2007
Computing drainage patterns for more realistic erosion
This paper suggests a way to estimate for each point the area of its watershed: hal.science/hal-04049125v1/document
By setting the rate of erosion to be proportional to the slope times the watershed area, we get a more realistic simulation of erosion.
Channels:
a: the height of the surface
b: perlin noise, so the results are less plastic-looking
c: the uplift channel: the whole surface is pushed upwards at this rate, to counteract the erosion
d: the drainage patterns we compute as we go
Run it for yourself in Ready: github.com/GollyGang/ready/blob/gh-pages/Patterns/KardarParisiZhang1986/drainage_erosion.vti
By setting the rate of erosion to be proportional to the slope times the watershed area, we get a more realistic simulation of erosion.
Channels:
a: the height of the surface
b: perlin noise, so the results are less plastic-looking
c: the uplift channel: the whole surface is pushed upwards at this rate, to counteract the erosion
d: the drainage patterns we compute as we go
Run it for yourself in Ready: github.com/GollyGang/ready/blob/gh-pages/Patterns/KardarParisiZhang1986/drainage_erosion.vti
Переглядів: 281
Відео
Erosion simulation with a simple PDE - the KPZ equation.
Переглядів 1,6 тис.4 місяці тому
Ricky Reusser recently discovered (mathstodon.xyz/@rreusser/111913990129998428) (or rediscovered?) that with a negative coefficient in the gradient magnitude term of the KPZ equation (www.mit.edu/~kardar/research/seminars/Growth/talks/Kyoto/KPZ.html) you could get a nice-looking simulation of hydraulic erosion. And the equation couldn't be simpler. One term smooths the height image, the other d...
A space-filling polyhedron, based on the Weaire-Phelan foam
Переглядів 518Рік тому
The Weaire-Phelan foam is a relaxation of a packing of irregular dodecahedra and tetrakaidecahedra. Dissect the dodecahedra into pentagon-based pyramids by adding a vertex at the center, then glue their bases to the surrounding tetrakaidecahedra. Amazingly the faces line up and the result is a decahedron that tiles space by itself. This was discovered in 2007 by Guy Inchbald and Roger Kaufman, ...
Voronoi Honeycombs
Переглядів 542Рік тому
Animates between six different space-filling polyhedra: the cubic lattice, the A15 crystal (Weaire-Phelan), body-centered cubic (truncated octahedra), the Laves graph (triamond), face-centered cubic (rhombic dodecahedra), and diamond cubic (triakis truncated tetrahedra). In the lower-left is shown the unit cell, with 8 cell centers and two of the polyhedra shown in wireframe. On each frame we m...
Transforming a Kleinian group
Переглядів 5202 роки тому
The pattern is the limit set of a Kleinian group of two Möbius transformations and their inverses. By applying fractional powers of each transform we can show how they map the set onto itself. This self-similarity is what gives rise to its fractal nature. Play here: timhutton.github.io/mobius-transforms/dfs_recipes.html Kleinian groups: en.wikipedia.org/wiki/Kleinian_group Möbius transformation...
Iterating the Möbius transformation
Переглядів 4332 роки тому
My Möbius transformation explorer now allows you to draw on the screen. timhutton.github.io/mobius-transforms/ A Möbius transformation is f(z) = (az b) / (cz d) where z, a, b, c and d are complex numbers. Multiple copies of the drawing are shown, by applying multiple iterations of the Möbius transformation and its inverse. The final view shows the stereographic projection onto the Riemann spher...
Neatly stacked cats
Переглядів 2803 роки тому
I don't know how they got themselves into this position. The whole time Whisper is pretending that she has no idea what is happening. 😹
The Korteweg-de Vries equation (1895)
Переглядів 1,2 тис.3 роки тому
The Korteweg-de Vries equation (1895) is a model of shallow water waves. en.wikipedia.org/wiki/Korteweg–de_Vries_equation da/dt = -0.5 * a * da/dx - d³a/dx³ How do the waves manage to pass through each other!? Simulated as 256 floats. One of the new patterns in Ready 0.11.0: github.com/GollyGang/ready
Bistability in the stabilized Kuramoto-Sivashinsky equation
Переглядів 4153 роки тому
The Kuramoto-Sivashinsky equation, with its range stabilized based on advice from Steffen Richters. Pattern created by Dan Wills. Video made in Ready: github.com/GollyGang/ready The equation is: da/dt = 0.2 * gradient_magnitude_squared(a) - bilaplacian(a) - laplacian(a) - 0.05 * a On the right is an image of the values, drawn using the color scale at the bottom. On the left is a surface plot of...
The Mandelbrot set is a churning machine
Переглядів 17 тис.3 роки тому
Its job is to fling off the red pixels and hang onto the green ones. This video shows the orbits for every pixel, linearly interpolated between each iteration. Points that will eventually fly off to infinity are colored red from the beginning. The green points all stay nearby forever. Thus the 'job' of the Mandelbrot set is to fling off the red pixels and hang onto the green ones. Here's the sa...
Gravity is not a force - varying gravitational field strength, inertial frame
Переглядів 2263 роки тому
Interactive web app: timhutton.github.io/GravityIsNotAForce/variable_gravity.html Under general relativity, gravity is not a force. Instead inertial objects (those that are free to fall) move along straight lines in spacetime. A planet causes spacetime to distort, which causes the straight lines paths to converge. This makes it look as if the objects are being pulled towards the planet by some ...
Applying the Mandelbrot mapping: inside the set is green, outside is red
Переглядів 2,6 тис.3 роки тому
Source code: github.com/timhutton/mandelstir The Mandelbrot z^2 c mapping is applied to every point in the radius-2 disk, with linear interpolation between iterations to show how the points move. Points that belong to the Mandelbrot set are colored in green, while those outside are colored red and eventually disappear as they move off to infinity. The background image, in dark blue, shows the M...
Applying the Mandelbrot mapping to the points outside the set
Переглядів 1,6 тис.3 роки тому
Source code: github.com/timhutton/mandelstir The Mandelbrot z^2 c mapping is applied to every point outside the Mandelbrot set, with linear interpolation between iterations to show how the points move. Eventually all of these points disappear as they move off to infinity. The background image, in dark blue, shows the Mandelbrot set. The red overlay shows the density of the points being tracked....
Applying the Mandelbrot mapping to the top bulb
Переглядів 1,1 тис.3 роки тому
Source code: github.com/timhutton/mandelstir The Mandelbrot z^2 c mapping is applied to every point in the circle to the top of the main cardioid, with linear interpolation between iterations to show how the points move. Points in this region fall into period-3 orbits. The background image, in dark blue, shows the full set. The green overlay shows the density of the points being tracked.
Applying the Mandelbrot mapping to the front bulb
Переглядів 1 тис.3 роки тому
Source code: github.com/timhutton/mandelstir The Mandelbrot z^2 c mapping is applied to every point in the circle to the left of the main cardioid, with linear interpolation between iterations to show how the points move. Points in this region fall into period-2 orbits, alternating location every frame. The background image, in dark blue, shows the full set. The green overlay shows the density ...
Applying the Mandelbrot mapping to the main cardioid
Переглядів 1,5 тис.3 роки тому
Applying the Mandelbrot mapping to the main cardioid
Gravity is not a force - varying gravitational field strength, escape velocity
Переглядів 1113 роки тому
Gravity is not a force - varying gravitational field strength, escape velocity
Gravity is not a force - varying gravitational field strength
Переглядів 943 роки тому
Gravity is not a force - varying gravitational field strength
Gravity is not a force - accelerating reference frames
Переглядів 1883 роки тому
Gravity is not a force - accelerating reference frames
Morosov2008 multi-species reaction-diffusion
Переглядів 5354 роки тому
Morosov2008 multi-species reaction-diffusion
Three space-filling shapes hiding in the structure of diamond
Переглядів 2 тис.6 років тому
Three space-filling shapes hiding in the structure of diamond
Skiing in La Tania, from top to bottom.
Переглядів 1,2 тис.7 років тому
Skiing in La Tania, from top to bottom.
What, that's not a bilayer...
What arethe rules of simulation?
IT SOUNDS LIKE NUMBERBLOCKS JUMPSCARES🤓
what the hell is this Fractal????
Buddhabrot
can u mix the maps with diffrent colors or layers and blend it ?
What do you want to achieve? If you want photorealism you probably want to import the results into a proper renderer.
Nice results!
I don’t think that the last case accurately models snowfall. Snow does not come to rest where the gradient is higher. Rather it is deposited evenly at first, then may be redistributed by wind, accumulating in regions of low wind speed. And it may be redistributed by avalanches.
Although on small scales where snow is whirling about and more likely to settle perpendicular to surfaces than purely vertically from gravity, I would agree that your model could be applicable. Great simulation anyhow!
This seems a bit similar to this work: ua-cam.com/video/gCP7jzcPLyQ/v-deo.html They get rivers and creeks, which you don't really seem to get, but I think your ridges look better than theirs.
Thanks for this. Looks like they have the same equation but with multiplier on the gradient term given by the drainage area, which is pretty cool and is presumably why they get rivers.
I had a go at implementing their method for computing the drainage area. It gives nice results. ua-cam.com/video/MBXdy44lEbI/v-deo.html
Nice finding! Did you use a negative value only for lambda? en.wikipedia.org/wiki/Kardar%E2%80%93Parisi%E2%80%93Zhang_equation
Yes, exactly.
I like the song! It's a smoooooooth life
Original research on this concept: "Toroidal Game of Life" by Ole Nelson, Grinnell College, 2000. I can't find the research online, but I made some very insignificant contributions to it. I'm sure she would be thrilled to know that someone else made a better implementation! I'm sharing this with my students.
Mandelbrot decides to run really fast
Mandelbrot calms down after becoming angry
topologists: 3 hole donut
Very cool. Would love to the same thing but with a hexagonal grid.
A+
Also the octahedron fills all of space. I wonder the proof of these carbon atoms, like how do you know where they are really?
The regular octahedron can't fill space. For that you need truncated octahedra: en.wikipedia.org/wiki/Bitruncated_cubic_honeycomb
@@tim_huttonyou are only partially correct. A regular octahedron is not space filling, but if you squish it just on the right amount it will be. It consists of the triangles with two 54.735 and one 70.529 degrees approximately. Stacking 6 of these squished octahedrons will give you a rhombic tetrahedron.
Please, tell what kind of model did you use in this simulation.
This is github.com/GollyGang/ready/blob/gh-pages/Patterns/Experiments/TimHutton/mutually-catalytic_spots.vti which you can open in Ready. It's a 4-chemical reaction-diffusion system.
@@tim_hutton thanks for reply 😉
Smooth Life is interesting.
It's cats all the way down.
The cosmic web
Looks cyriak's animation
It'd probably take me quite a bit of time to wrap my head around all of what's going on here. But I do really enjoy the animation!
It's almost magical in a way. I haven't quite wrapped my mind around how you're doing the transformation, but perhaps that's even for the best. Why spoil a pleasant dream?
This reminds me a lot of Electric Sheep, and it's so mesmerizing to watch!
Extremely trippy; I love it!
This was...hexagon-awesome!
I wasn't Ready for how cool that looked.
This was...torustastic! 👍
It was nice to hear some music with this one, and it was very fitting and overall the animation was very relaxing. Thank you for sharing! 👍
I was recently recommended your work by Dave Ackley, when I asked him if he know of any similar projects to his Movable Feast Machine. Your work seems fascinating, especially since it had already been conducted so long ago. By any chance, are you familiar with Dave's work, and if so, what do you think of it? I'm just a hobbyist and have tried to acquaint myself with the basics, so I always appreciate trying to get at the concepts and intuition. I'd also love to find (or find out about someone finding) the holy grail you mentioned someday...
Order arising out of chaos, always satisfying 👍
It's funny how you can start to imagine seeing objects in the patterns. To me, this looked like a radiator grill.
This is super useful. Do either of these correspond to the kissing number of 12 for 3 dimensions? I need/want a tessellating polytope where all instances that meet at a vertex also share edges/faces. Like hex-grids and unlike square-grids
I'm not sure what you mean by kissing number in the context of polyhedra. Usually it's about spheres. I think you want a tiling where no two tiles join only at a vertex. Examples include: Weaire-Phelan (the A15 crystal, the first one in the video), truncated octahedra, the Laves graph (I think), diamond cubic (I think). The simplest and most pleasing one is the truncated octahedral tiling: en.wikipedia.org/wiki/Bitruncated_cubic_honeycomb Non-examples include: rhombic dodecahedra, cubes, the decahedral tiling in the video above. A video that shows these: ua-cam.com/video/OlRSXm6Pt9k/v-deo.html
@@tim_hutton perfect response thank you!
This was not meant for human eyes.
Wonderful, congratulations. I have come up with another monotiling, derived from Weaire-Phelan, which I hope to taunt you with in the near future.
For anyone coming here and seeing this comment, I just want to point out that this was not some random bullshit from a spammer, this was the real deal. This user (Guy Inchbald) really did have a new unseen monotile that he shared with me. mathstodon.xyz/@timhutton/109659177990308971 Amazing!
What devilry is this?
So, just wraparound game of life.
"Conway's Game of Life on a Torus" me: "Conway's Game of Life on a donut"
0:20 regular show
What about Conway's game of life on a mandelbrot set?
Do it on an apeirogon
i'm uncomfortable of this video
Donut
Trypophobia to the max. Still cool though!
i just unearthed an internet fossil
Algorithm moment
Conway's game of bagels
it dongnuts nut rotrus🤬🤬🤬🤬🦀🦀🐠🐠🦕🦕🦎🦎
clickbait/s