Each point represents one eigenvalue from the spectrum of a random 5×5 matrix with entries from {-1,0,1}. Warmer colors show regions where eigenvalues cluster more densely.
#MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
#MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
May 3, 2025 at 9:36 PM
Each point represents one eigenvalue from the spectrum of a random 5×5 matrix with entries from {-1,0,1}. Warmer colors show regions where eigenvalues cluster more densely.
#MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
#MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -1.2-1.2i to 1.2+1.2i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
May 8, 2025 at 10:10 PM
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -1.2-1.2i to 1.2+1.2i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -0.28-0.28i to 0.28+0.28i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
May 13, 2025 at 10:08 PM
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -0.28-0.28i to 0.28+0.28i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
A density plot of Bohemian eigenvalues from 109.000 random 20×20 anti-tridiagonal matrices with entries in {-1,0,1}. Colors represent eigenvalue frequency; real eigenvalues are excluded. Viewed on [-2.5-2.5i, 2.5+2.5i].
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math #SciArt
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math #SciArt
May 5, 2025 at 9:48 PM
A density plot of Bohemian eigenvalues from 109.000 random 20×20 anti-tridiagonal matrices with entries in {-1,0,1}. Colors represent eigenvalue frequency; real eigenvalues are excluded. Viewed on [-2.5-2.5i, 2.5+2.5i].
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math #SciArt
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math #SciArt
Complex function visualization: 𝑓(𝑧)=𝑧
→ Hue encodes the phase (argument of 𝑓(𝑧))
→ Brightness encodes the fractional part of log2∣𝑓(𝑧)∣
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
→ Hue encodes the phase (argument of 𝑓(𝑧))
→ Brightness encodes the fractional part of log2∣𝑓(𝑧)∣
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
April 27, 2025 at 9:20 PM
Complex function visualization: 𝑓(𝑧)=𝑧
→ Hue encodes the phase (argument of 𝑓(𝑧))
→ Brightness encodes the fractional part of log2∣𝑓(𝑧)∣
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
→ Hue encodes the phase (argument of 𝑓(𝑧))
→ Brightness encodes the fractional part of log2∣𝑓(𝑧)∣
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Exploring the roots of 131.072 random ±1-polynomials of degree 16.
Each dot is a root, brightness shows how frequently it appears across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Each dot is a root, brightness shows how frequently it appears across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
April 29, 2025 at 11:24 PM
Exploring the roots of 131.072 random ±1-polynomials of degree 16.
Each dot is a root, brightness shows how frequently it appears across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Each dot is a root, brightness shows how frequently it appears across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Final Result - Complex function:
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
→ Hue encodes phase (arg f(z))
→ Brightness encodes log-magnitude (|f(z)|)
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
→ Hue encodes phase (arg f(z))
→ Brightness encodes log-magnitude (|f(z)|)
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
April 25, 2025 at 9:39 PM
Final Result - Complex function:
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
→ Hue encodes phase (arg f(z))
→ Brightness encodes log-magnitude (|f(z)|)
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
→ Hue encodes phase (arg f(z))
→ Brightness encodes log-magnitude (|f(z)|)
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
Exploring the roots of 131,072 polynomials with coefficients in {1,3}.
Each dot is a root of a degree-16 polynomial; brightness reveals its frequency across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Each dot is a root of a degree-16 polynomial; brightness reveals its frequency across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
May 1, 2025 at 12:14 AM
Exploring the roots of 131,072 polynomials with coefficients in {1,3}.
Each dot is a root of a degree-16 polynomial; brightness reveals its frequency across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Each dot is a root of a degree-16 polynomial; brightness reveals its frequency across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Visualizing roots of z² + (t₁ + t₂)
t₁ and t₂ are complex numbers, |t₁| = |t₂| = 1
Colors encode the angle of each t₁ and t₂
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
t₁ and t₂ are complex numbers, |t₁| = |t₂| = 1
Colors encode the angle of each t₁ and t₂
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
May 15, 2025 at 9:31 PM
Visualizing roots of z² + (t₁ + t₂)
t₁ and t₂ are complex numbers, |t₁| = |t₂| = 1
Colors encode the angle of each t₁ and t₂
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
t₁ and t₂ are complex numbers, |t₁| = |t₂| = 1
Colors encode the angle of each t₁ and t₂
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Complex function (magnitude visualization):
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
Absolute value of the same function from my previous post. The brightness represents the fractional part of log₂|f(z)|.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
Absolute value of the same function from my previous post. The brightness represents the fractional part of log₂|f(z)|.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
April 25, 2025 at 7:05 PM
Complex function (magnitude visualization):
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
Absolute value of the same function from my previous post. The brightness represents the fractional part of log₂|f(z)|.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
Absolute value of the same function from my previous post. The brightness represents the fractional part of log₂|f(z)|.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
Plot shows 211,416 eigenvalues in [-3-3i, 3+3i]. Total of 348,500 matrices. 21,456 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
#p5js #MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
The failures represent edge cases where numeric.js couldn't converge.
#p5js #MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
May 3, 2025 at 9:43 PM
Plot shows 211,416 eigenvalues in [-3-3i, 3+3i]. Total of 348,500 matrices. 21,456 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
#p5js #MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
The failures represent edge cases where numeric.js couldn't converge.
#p5js #MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
repost @erik_alan_norman on IG
2D vs 3D Möbius transformations. #möbius #transformations #geometry #complexanalysis #analysis #projection #sphere #math #maths #mathematics #mathematician #vector #calculus #blender #3dartist #3danimation #geometrynodes #fields
2D vs 3D Möbius transformations. #möbius #transformations #geometry #complexanalysis #analysis #projection #sphere #math #maths #mathematics #mathematician #vector #calculus #blender #3dartist #3danimation #geometrynodes #fields
June 16, 2025 at 9:01 AM
repost @erik_alan_norman on IG
2D vs 3D Möbius transformations. #möbius #transformations #geometry #complexanalysis #analysis #projection #sphere #math #maths #mathematics #mathematician #vector #calculus #blender #3dartist #3danimation #geometrynodes #fields
2D vs 3D Möbius transformations. #möbius #transformations #geometry #complexanalysis #analysis #projection #sphere #math #maths #mathematics #mathematician #vector #calculus #blender #3dartist #3danimation #geometrynodes #fields
Want to explore complex analysis in a more visual and interactive way? 🧠💻
Explore, visualise, and learn complex analysis interactively with this project:
complex-analysis.com
#ComplexAnalysis #Mathematics #MathEducation #Learning
Explore, visualise, and learn complex analysis interactively with this project:
complex-analysis.com
#ComplexAnalysis #Mathematics #MathEducation #Learning
September 18, 2026 at 1:51 AM
Want to explore complex analysis in a more visual and interactive way? 🧠💻
Explore, visualise, and learn complex analysis interactively with this project:
complex-analysis.com
#ComplexAnalysis #Mathematics #MathEducation #Learning
Explore, visualise, and learn complex analysis interactively with this project:
complex-analysis.com
#ComplexAnalysis #Mathematics #MathEducation #Learning
Plot shows 215,240 eigenvalues in [-2.5-2.5i, 2.5+2.5i]. Total of 109,000 matrices. 16,664 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
The failures represent edge cases where numeric.js couldn't converge.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
May 5, 2025 at 9:57 PM
Plot shows 215,240 eigenvalues in [-2.5-2.5i, 2.5+2.5i]. Total of 109,000 matrices. 16,664 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
The failures represent edge cases where numeric.js couldn't converge.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Just released: Proof of the Riemann Hypothesis via Haar inversion + functional equation + Peter-Weyl compactness.
Preprint:
doi.org/10.5281/zeno...
Feedback welcome!
#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros
Preprint:
doi.org/10.5281/zeno...
Feedback welcome!
#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros
January 8, 2026 at 10:32 AM
Just released: Proof of the Riemann Hypothesis via Haar inversion + functional equation + Peter-Weyl compactness.
Preprint:
doi.org/10.5281/zeno...
Feedback welcome!
#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros
Preprint:
doi.org/10.5281/zeno...
Feedback welcome!
#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros
Aquí va la primera demostración de la semana del teorema fundamental del álgebra. En esta se usa el Principio del Módulo Máximo: si la función holomorfa f toma su valor absoluto máximo en un conjunto abierto, entonces es constante.
#mathematics #matematicas
#algebra #complexanalysis
#mathematics #matematicas
#algebra #complexanalysis
April 15, 2025 at 3:51 AM
Aquí va la primera demostración de la semana del teorema fundamental del álgebra. En esta se usa el Principio del Módulo Máximo: si la función holomorfa f toma su valor absoluto máximo en un conjunto abierto, entonces es constante.
#mathematics #matematicas
#algebra #complexanalysis
#mathematics #matematicas
#algebra #complexanalysis
Este semestre estoy dando el curso Análisis Complejo, donde estudiamos las propiedades del plano complejo y de las funciones holomorfas.
#matemáticas #mathematics #math #algebra #complexanalysis
#matemáticas #mathematics #math #algebra #complexanalysis
April 15, 2025 at 3:43 AM
Este semestre estoy dando el curso Análisis Complejo, donde estudiamos las propiedades del plano complejo y de las funciones holomorfas.
#matemáticas #mathematics #math #algebra #complexanalysis
#matemáticas #mathematics #math #algebra #complexanalysis
🧑🎓💼1 postdoc position is open in #Probability at the University of Rome La Sapienza, within the FIS 2 project Understanding pattern formation in nature via #complexanalysis, PI Vittoria Silvestri.
Deadline for applications: 29 August 2025 - strict
web.uniroma1.it/trasparenza/...
Deadline for applications: 29 August 2025 - strict
web.uniroma1.it/trasparenza/...
Bando n. 2/2025 per n. 1 Contratto di ricerca - GSD 01/MAT-03 - SSD MATH-03/B - Resp. scientifico Prof.ssa Silvestri (SPC: 2025-2791-1344-236697) | Amministrazione trasparente
web.uniroma1.it
August 15, 2025 at 10:12 AM
🧑🎓💼1 postdoc position is open in #Probability at the University of Rome La Sapienza, within the FIS 2 project Understanding pattern formation in nature via #complexanalysis, PI Vittoria Silvestri.
Deadline for applications: 29 August 2025 - strict
web.uniroma1.it/trasparenza/...
Deadline for applications: 29 August 2025 - strict
web.uniroma1.it/trasparenza/...
Newton fractal — f(z) = z³ − 1. Three cube roots of unity as attractors. Each point colored by which root Newton's method converges to; shaded by convergence speed. The fractal boundary appears where all three basins meet — at every scale. #generativeart #mathematics #fractal #complexanalysis
February 28, 2026 at 8:18 AM
Newton fractal — f(z) = z³ − 1. Three cube roots of unity as attractors. Each point colored by which root Newton's method converges to; shaded by convergence speed. The fractal boundary appears where all three basins meet — at every scale. #generativeart #mathematics #fractal #complexanalysis
The #math department at #purduefortwayne 🐘 welcomes two new tenure-track faculty!
Vahan Mkrtchyan's research is in #graphtheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #complexanalysis and geometric analysis
Vahan Mkrtchyan's research is in #graphtheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #complexanalysis and geometric analysis
August 12, 2025 at 5:43 PM
The #math department at #purduefortwayne 🐘 welcomes two new tenure-track faculty!
Vahan Mkrtchyan's research is in #graphtheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #complexanalysis and geometric analysis
Vahan Mkrtchyan's research is in #graphtheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #complexanalysis and geometric analysis
Toupin, D. (2025). Holding the Line: How Haar Measure, Functional Symmetry, and Compactness Force the Riemann Hypothesis. Zenodo. doi.org/10.5281/zeno...
#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems
#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems
Holding the Line: How Haar Measure, Functional Symmetry, and Compactness Force the Riemann Hypothesis
We prove that all non-trivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2. We establish this result via three independent proofs using different mathematical framework...
doi.org
January 26, 2026 at 5:47 PM
Toupin, D. (2025). Holding the Line: How Haar Measure, Functional Symmetry, and Compactness Force the Riemann Hypothesis. Zenodo. doi.org/10.5281/zeno...
#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems
#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems
I've submitted my abstract for a talk at #jmm2027 in #chicago - assuming it's accepted, I will be speaking about the inhomogeneous Cauchy-Riemann equation. I also signed up to judge some student posters. See you there??
#riemann200 #mathconference #complexanalysis :gauss:
#riemann200 #mathconference #complexanalysis :gauss:
September 16, 2026 at 7:45 PM
I've submitted my abstract for a talk at #jmm2027 in #chicago - assuming it's accepted, I will be speaking about the inhomogeneous Cauchy-Riemann equation. I also signed up to judge some student posters. See you there??
#riemann200 #mathconference #complexanalysis :gauss:
#riemann200 #mathconference #complexanalysis :gauss:
From my #icm2026 talk today- I don't know whether the "all sessions will be recorded and ... available online" plan applies to the short communications.
#complexanalysis
#complexanalysis
July 29, 2026 at 2:05 AM
From my #icm2026 talk today- I don't know whether the "all sessions will be recorded and ... available online" plan applies to the short communications.
#complexanalysis
#complexanalysis
Reading about curves makes me so antsy to go revise #ComplexAnalysis
March 19, 2024 at 12:53 AM
Reading about curves makes me so antsy to go revise #ComplexAnalysis
Jordan’s Lemma bounds integrals over large semicircles in the complex plane, ensuring exponential terms decay and making residue calculus and Fourier methods work smoothly. Do you remember using it?
#ComplexAnalysis #Mathematics #STEM #MathEducation #MathType
#ComplexAnalysis #Mathematics #STEM #MathEducation #MathType
March 2, 2026 at 1:00 PM
Jordan’s Lemma bounds integrals over large semicircles in the complex plane, ensuring exponential terms decay and making residue calculus and Fourier methods work smoothly. Do you remember using it?
#ComplexAnalysis #Mathematics #STEM #MathEducation #MathType
#ComplexAnalysis #Mathematics #STEM #MathEducation #MathType