barqueira

Roots of complex polynomial
Inspired by ‪the work of @sconradi.bsky.social
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Bem engraçado.

My bear phase.
#CorgiCrew #DogsOfBluesky #corgisky #corgi #photography #photo

Father and son in complete harmony.
#CorgiCrew #DogsOfBluesky #corgisky #corgi #photography #photo

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It sounds great.

Yes, It is done with Python.

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Exploring the roots of an 18th-degree complex polynomial x^18−x^17+(100it1^5−100it1^4+100it1^3−100it1^2−100t1+100i)·x^10+(−100it2^4−100it2^3+100it2^2+100it2+100)·x^6−0.1 x+0.1 where t₁,t₂ are complex numbers on the unit circle. z-axis and color encode Im(t1).

Roots of complex polynomial
Inspired by ‪the work of @sconradi.bsky.social
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Ria Formosa, Santa-Luzia, #Tavira, #Algarve, #Portugal
July, 2025
#photography, #photo

It is beautiful.

Hopalong Attractor
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Exploring the chaotic beauty of Hopalong Attractors. Each of these nine images is generated from a different set of parameters, showing the incredible variety of patterns that emerge.
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Visualizing Laplace Eigenfunctions on a Circular Domain
These vibrational patterns emerge from solving the eigenvalue problem for the discrete Laplacian matrix.
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Photo taken by my youngest son of our great bud.
#Photography

A new approach:
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Visualizing the roots of:
x⁹ + 3x⁷ + (−25𝑖𝑡₂² −25𝑖𝑡₂ +75𝑖)x⁵ −4x −50𝑡₁ −50𝑖
where 𝑡₁, 𝑡₂ are random points on the complex unit circle
750,000 (𝑡₁,𝑡₂) pairs → 6.75 million roots
Color maps Im(𝑡₂) using a psychedelic rainbow gradient
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

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Visualizing roots of::
(-15i·t₂² -15i·t₂ +15i)x⁷ + 3x⁶ -100t₁ -100i
where t₁, t₂ are complex numbers with |tⱼ|=1.
Key to the plot:
• ↔️ x/y: Root's real/imaginary parts
• ↕️ z: Imaginary part of t₂
• 🔵→🔴 Colors: Im(t₂) from -1 (blue) to +1 (red)
#MathArt #Python #CodeArt #SciArt #CreativeCoding #Math

Color & Height:
z-axis = Im(t₂) (vertical)
Colors (YlOrRd colormap) = Im(t₂)
Yellow: Im(t₂) ≈ 0 (t₂ nearly real)
Red: Im(t₂) → 1 (t₂ almost purely imaginary)

3D visualization shows the complex roots of:
10x¹⁸ - 10x¹⁷ + (3200t₂⁶-4800t₂⁴+1800t₂²-100)x⁸ + (200t₁³-100)x⁷ - 10x + 10
where t₁,t₂ are complex numbers on the unit circle.
Colors represent Im(t₂) ≥ 0
Inspired by ‪the work of @sconradi.bsky.social
#MathArt #Python #CodeArt #BlueskyArt #SciArt

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Yesterday in Ria Formosa, Santa-Luzia, Tavira, Portugal
#Photography, #Portugal, #Algarve, #tavira

Another perspective to emphasize 3D dimentions, with the x, y, z axes.
#MathArt #Python #CodeArt #BlueskyArt #SciArt

Equation:
8x⁴ + (t₂⁴ − i·t₂² − 1)x² + t₁⁴ + t₁² − i·t₁ − 1
where |t₁| = |t₂| = 1
The z-axis and color both encode the phase of t₂.

3D plot of the roots of a random family of quartic polynomials with complex coefficients on the unit circle.
The z-axis and color both encode the phase of 𝑡2.
Inspired by ‪@sconradi.bsky.social work.
#MathArt #Python #CodeArt #BlueskyArt #SciArt

4000 Line Segments - Symmetry from Nested Sine Waves
Each segment’s position is controlled by layered trigonometric functions.
#MathArt #Python #CodeArt #BlueskyArt #SciArt #CreativeCoding #GenerativeArt