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Cliff Pickover

@pickover • 234,145 subscribers

Increase your sense of wonder. (Author of 50 books & 800 patents. Yale Ph.D.) "Pickover contemplates realms beyond our known reality." ~NY Times

Shorts

Engineering, mathematics. Unconventional gears. The center of a logarithmic spiral traces a straight line as it is rolled. By Matt Henderson, Matt Henderson, used with permission.

Engineering, mathematics. Unconventional gears. The center of a logarithmic spiral traces a straight line as it is rolled. By Matt Henderson, Matt Henderson, used with permission.

1,467,686 Aufrufe

I created a new animation of the amazing "Fibonacci Elephant." (It uses more squares in the trunk than in the previous animation I posted, suggesting an infinite trunk.) Credit: By Daniel Mentrard, Daniel Mentrard, Used with permission, [math]

I created a new animation of the amazing "Fibonacci Elephant." (It uses more squares in the trunk than in the previous animation I posted, suggesting an infinite trunk.) Credit: By Daniel Mentrard, Daniel Mentrard, Used with permission, [math]

93,390 Aufrufe

Mathematics, physics, mechanical linkage mechanism. "Double Hoberman Mechanism." By 上木敬士郎 / Keishiro Ueki, 上木敬士郎 / Keishiro Ueki, Used with permission.

Mathematics, physics, mechanical linkage mechanism. "Double Hoberman Mechanism." By 上木敬士郎 / Keishiro Ueki, 上木敬士郎 / Keishiro Ueki, Used with permission.

16,253 Aufrufe

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

53,369 Aufrufe

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

27,768 Aufrufe

Mathematics and Mystery. Fourier Decomposition of a Pentagram. By George Savva, Used with permission.

Mathematics and Mystery. Fourier Decomposition of a Pentagram. By George Savva, Used with permission.

54,335 Aufrufe

Mathematics. The infinite race. The "Penrace Triangle." Eternity, hyperspace, forever. By Linus Dahlgren, Linus Dahlgren, Used with permission,

Mathematics. The infinite race. The "Penrace Triangle." Eternity, hyperspace, forever. By Linus Dahlgren, Linus Dahlgren, Used with permission,

33,434 Aufrufe

$Mathematics. A close look at the infinite swirling of the Rössler Attractor, which exhibits chaotic dynamics and fractal properties. Like a cosmic taffy-pulling machine. By Marcus Volz, Used with permission.$

Mathematics. A close look at the infinite swirling of the Rössler Attractor, which exhibits chaotic dynamics and fractal properties. Like a cosmic taffy-pulling machine. By Marcus Volz, Used with permission.

24,739 Aufrufe

World map shows global population distribution by latitude and longitude. (Will this be very different in 50 years?) By Engaging Data, Used with permission.

World map shows global population distribution by latitude and longitude. (Will this be very different in 50 years?) By Engaging Data, Used with permission.

85,181 Aufrufe

Mathematics, algorithms, spirals, geometry, programming. "The Hidden Music of Concentric Souls." Rotational Moiré Interference from Phase-Shifted Polar Sources. Animation by A. L. Crego, Used with permission

Mathematics, algorithms, spirals, geometry, programming. "The Hidden Music of Concentric Souls." Rotational Moiré Interference from Phase-Shifted Polar Sources. Animation by A. L. Crego, Used with permission

72,707 Aufrufe

Mathematics and mystery. "Two Ellipses." By Idan Tal, Idan Tal, Used with permission

Mathematics and mystery. "Two Ellipses." By Idan Tal, Idan Tal, Used with permission

53,426 Aufrufe

Math. A rare peek from within a "Gyroid," a fascinating minimal surface in geometry that separates space into two oppositely congruent labyrinths of passages. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. This infinitely extending "labyrinth" surface divides all of space into two identical, intertwined, mirror-image passages: without ever intersecting itself. Discovered by mathematician Alan Schoen in 1970, it's a triply periodic minimal surface (zero mean curvature everywhere, like a soap film), with no straight lines or mirror symmetry. It can be approximated by the surprisingly simple equation: sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0. Nature loves it too: gyroid nanostructures in butterfly wing scales create iridescent colors through light interference, and similar forms appear in cell membranes, polymers, and even ketchup-like fluids. It's a superstar in materials science for lightweight, strong 3D-printed structures and photonic crystals.

Math. A rare peek from within a "Gyroid," a fascinating minimal surface in geometry that separates space into two oppositely congruent labyrinths of passages. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. This infinitely extending "labyrinth" surface divides all of space into two identical, intertwined, mirror-image passages: without ever intersecting itself. Discovered by mathematician Alan Schoen in 1970, it's a triply periodic minimal surface (zero mean curvature everywhere, like a soap film), with no straight lines or mirror symmetry. It can be approximated by the surprisingly simple equation: sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0. Nature loves it too: gyroid nanostructures in butterfly wing scales create iridescent colors through light interference, and similar forms appear in cell membranes, polymers, and even ketchup-like fluids. It's a superstar in materials science for lightweight, strong 3D-printed structures and photonic crystals.

41,176 Aufrufe

Mathematics. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

Mathematics. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

52,351 Aufrufe

Electronics, physics. → What is the name of this kind of switch, and what purpose does it serve? Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “412Couchloc” (Jul 20, 2026).

Electronics, physics. → What is the name of this kind of switch, and what purpose does it serve? Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “412Couchloc” (Jul 20, 2026).

17,689 Aufrufe

Visualization by Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. Physicist Roger Penrose wrote: "Everything in the physical Universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations... or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’.... Even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles." ~ The Road to Reality Belloni visualization employs 256K particles.

Visualization by Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. Physicist Roger Penrose wrote: "Everything in the physical Universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations... or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’.... Even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles." ~ The Road to Reality Belloni visualization employs 256K particles.

29,315 Aufrufe

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

136,542 Aufrufe

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Used with permission.

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Used with permission.

17,098 Aufrufe

Mathematics. Spiral. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

Mathematics. Spiral. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

15,432 Aufrufe

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Source: Used with permission.

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Source: Used with permission.

119,270 Aufrufe

Mathematics. Two spheres, rolling on a strange track, for an eternity. By Matthew Hughes, Matthew Hughes, Used with permission.

Mathematics. Two spheres, rolling on a strange track, for an eternity. By Matthew Hughes, Matthew Hughes, Used with permission.

19,446 Aufrufe

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The year is 2020. This infographic animation caught my eye today. Spreading of Covid-19. Source: CC BY-NC-SA 4.0

The year is 2020. This infographic animation caught my eye today. Spreading of Covid-19. Source: CC BY-NC-SA 4.0

299,046 Aufrufe • vor 28 Tagen

Strange Universe. Math, Physics, Reality. "6 belts are anchored on the outside to a fixed frame, and on the inside to a spinning cube. Although the cube spins continuously in one direction the belts never become tangled. The belts return to their original configuration when the cube has rotated 720 degrees." - Jason Hise,

Strange Universe. Math, Physics, Reality. "6 belts are anchored on the outside to a fixed frame, and on the inside to a spinning cube. Although the cube spins continuously in one direction the belts never become tangled. The belts return to their original configuration when the cube has rotated 720 degrees." - Jason Hise,

887,759 Aufrufe • vor 3 Monaten

Mathematical Coalescence. Math machine. A strange pattern emerges in these Archimedean Spirals with interconnecting tubes. "The pattern 東南西北 can be displaced, but remains conserved." By Raven Kwok, Raven Kwok, Used with permission

Mathematical Coalescence. Math machine. A strange pattern emerges in these Archimedean Spirals with interconnecting tubes. "The pattern 東南西北 can be displaced, but remains conserved." By Raven Kwok, Raven Kwok, Used with permission

166,592 Aufrufe • vor 3 Monaten

Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

1,843,124 Aufrufe • vor 3 Jahren

For the mathematicians you love.... Examples of parametric curves. By Jerome White, Jerome White, Used with permission.

For the mathematicians you love.... Examples of parametric curves. By Jerome White, Jerome White, Used with permission.

70,033 Aufrufe • vor 1 Monat

Physics, mathematics, engineering, witchcraft. Welcome to the Twilight Zone. By Physicsfun, Used with permission.

Physics, mathematics, engineering, witchcraft. Welcome to the Twilight Zone. By Physicsfun, Used with permission.

19,147 Aufrufe • vor 15 Tagen

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

53,369 Aufrufe • vor 1 Monat

Unpredictable universe? This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester, Feb 4, 2018): Source 2 (Matlab code): Wayback:

Unpredictable universe? This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester, Feb 4, 2018): Source 2 (Matlab code): Wayback:

24,482 Aufrufe • vor 1 Monat

Mathematics. Epicycles. Fourier series. Polar bear synthesis. By Daniel Mentrard, Daniel Mentrard, Used with permission.

Mathematics. Epicycles. Fourier series. Polar bear synthesis. By Daniel Mentrard, Daniel Mentrard, Used with permission.

67,671 Aufrufe • vor 4 Monaten

Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)

Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)

496,511 Aufrufe • vor 3 Jahren

Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:

Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:

107,857 Aufrufe • vor 8 Monaten

Mathematical marvels, mysteries, and magic. Geometry and the eternal. Shock your friends. Determine the center of a drawn circle without a straightedge or compass. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

Mathematical marvels, mysteries, and magic. Geometry and the eternal. Shock your friends. Determine the center of a drawn circle without a straightedge or compass. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

21,611 Aufrufe • vor 1 Monat

Glimpse of hyperspace. Regular "4-Polytopes" (4-D objects, like the tesseract or hypercube). 4-D analogues of Platonic solids. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video within the 𝕏 stream of “友”, 𝕏 ID “tomo_” (Sep 21, 2026)

Glimpse of hyperspace. Regular "4-Polytopes" (4-D objects, like the tesseract or hypercube). 4-D analogues of Platonic solids. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video within the 𝕏 stream of “友”, 𝕏 ID “tomo_” (Sep 21, 2026)

13,609 Aufrufe • vor 24 Tagen

Mathematics. Our complicated, seemingly unpredictable universe. This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester): Source 2 (Matlab code):

Mathematics. Our complicated, seemingly unpredictable universe. This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester): Source 2 (Matlab code):

381,341 Aufrufe • vor 3 Jahren

Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.

Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.

333,438 Aufrufe • vor 3 Jahren

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

83,083 Aufrufe • vor 9 Monaten

Mathematics. Hidden inside every square is a 3-4-5 right triangle, which humans can reveal in the following manner. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

Mathematics. Hidden inside every square is a 3-4-5 right triangle, which humans can reveal in the following manner. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

70,753 Aufrufe • vor 9 Monaten

Strange Universe. Math, Physics, Reality. "12 strands are anchored on the outside to a fixed frame, and on the inside to a spinning dodecahedron. Although the dodecahedron spins continuously in one direction, the strands never become tangled. The strands return to their original configuration when the dodecahedron has rotated 720 degrees." - Jason Hise,

Strange Universe. Math, Physics, Reality. "12 strands are anchored on the outside to a fixed frame, and on the inside to a spinning dodecahedron. Although the dodecahedron spins continuously in one direction, the strands never become tangled. The strands return to their original configuration when the dodecahedron has rotated 720 degrees." - Jason Hise,

23,515 Aufrufe • vor 2 Monaten

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

20,741 Aufrufe • vor 2 Monaten

Mathematics, topology, geometry, simulation, algorithms. Watch this Cosmic Eversion Loop. Particle Tube Metamorphosis. Notice how the interior surface of the tube evaginates to become the "exterior." By Acid Boy 💊, Used with permission.

Mathematics, topology, geometry, simulation, algorithms. Watch this Cosmic Eversion Loop. Particle Tube Metamorphosis. Notice how the interior surface of the tube evaginates to become the "exterior." By Acid Boy 💊, Used with permission.

56,366 Aufrufe • vor 10 Monaten