Simone Conradi
@S_Conradi
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Theoretical Physics Ph.D., Computer Science Teacher. Author of “Intelligenza Artificiale” Zanichelli 2022. I draw using mathematics.
Anywhere
Joined December 2014
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It's because of this wonderful novel, "Maniac" by Benjamín Labatut published in Italy by
@adelphiedizioni
, that I came across the figure of the Italian physicist Nils Aall Barricelli, who really existed, and I tried to reproduce his pioneering
#Alife
simulations in
#Python
.
4
8
109
x>0 breaks the symmetry of the eigenvalues distribution.
Made with
#python
,
#matplotlib
and
#numpy
.
52
396
3K
40
405
3K
18
227
2K
14
150
1K
19
261
2K
18
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1K
Inspired by the wonderful "Computational Discovery on Jupyter" by By Neil J. Calkin, Eunice Y.S. Chan, and
@corless_rob
and the gallery of . Each plot represents eigenvalues of the corresponding matrix.
Made with
#python
,
@matplotlib
and
@numpy_team
.
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1K
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123
1K
17
117
1K
19
90
1K
15
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936
2
71
616
How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
12
111
922
11
76
859
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
9
108
839
9
74
811
10
72
814
Ten million random walks on SL_2(ℤ) in the upper-half complex plane and then mapped to the unit disc by z→(z-i)/(z+i). Each walk starts from a point inside the fundamental domain of SL_2(ℤ).
Made with
#python
,
#matplotlib
and
#numpy
.
8
86
816
Animated action of the complex function z⁴: ℂ → ℂ acting on a circle grid.
#complexnumbers
#complexfunctions
#python
#numpy
#matplotlib
#mathematics
#math
#Steam
#STEM
14
126
781
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below.
Made with
#python
,
#matplotlib
and
#numpy
.
6
133
786
For those who wanted the code, it is available (and also improvable) at this link:
In this brief article, you will find some additional explanations about eigenvalues figures:
12
130
773
Ten million random walks on SL_2(ℤ) in the upper-half complex plane. Each walk starts from a point inside the fundamental domain of SL_2(ℤ).
Made with
#python
,
#matplotlib
and
#numpy
.
11
77
713
11
87
698
Energy landscape of a Particle
#Lenia
simulation with two merging creatures made of different particles.
Made with
#python
,
@matplotlib
and Apple
#MLX
.
Inspired by
#Alife
11
117
675
18
145
1K
7
58
631
2
52
439
11
81
624
Roots of parametric polynomials.
A simple case.
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
3
84
601
9
44
604
Generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below. Made with
#python
,
#matplotlib
and
#numpy
.
12
67
590
22
52
578
An image of a fractal created using Halley's root-finding method.
Made with python, numpy and matplotlib.
6
61
560
4
54
543
3
75
537
Color version of "How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?"
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
7
70
529
How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
2
51
514
A symmetric attractor of a 𝑫ₙ equivariant map ℂ→ℂ. In this case n=5.
Made with
#python
,
#matplotlib
and
#numpy
.
11
58
498
A zoo of symmetric attractors of 𝑫ₙ equivariant maps ℂ→ℂ.
Made with
#python
,
#matplotlib
and
#numpy
.
11
61
481
A fractal plant generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below. Made with
#python
,
#matplotlib
and
#numpy
.
9
48
467
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
7
81
466
Energy landscape of a Particle
#Lenia
simulation.
Made with
#python
,
#matplotlib
and Apple
#MLX
. Inspired by
15
86
469
In mathematics, a rose curve is a sinusoid characterized by the equation r = cos(kθ) or r = sin(kθ) in polar coordinates
20
418
2K
3
61
464
4
72
454
Each frame is generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below. Made with
#python
,
#matplotlib
and
#numpy
.
10
49
449
5
62
459
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
4
65
447
12
58
450
A big avalanche in the simulation of the Bak-Tang-Wiesenfeld model of self-organized criticality.
Made with
#Python
,
#matplotlib
, and
#numpy
.
7
71
451
2
71
426
8
35
423
Artificial diatoms.
They are symmetric attractors of 𝑫ₙ equivariant maps ℂ→ℂ. 𝑫ₙ is the group of symmetries of a regular polygon.
The generic map is shown in the title of the figure.
Made with
#python
,
#matplotlib
and
#numpy
.
10
68
428
10
69
424
Exploring similarity fractal dimensions using Koch curves: from 1D to 2D.
Made with
#python
,
#matplotlib
, and
#numpy
.
4
66
422
Roots of parametric polynomials.
A simple case.
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
1
64
414
A contour plot depicting the absolute value of the numerical solution to the Feigenbaum-Cvitanović functional equation in the complex plane.
A gem of chaos theory.
Made with
#python
,
#matplotlib
and
#numpy
.
10
66
393
Another one for 3x3 matrices, with parameters on a torus. Gershgorin circles are in red. Made with
#python
,
#matplotlib
and
#numpy
.
4
42
398
Inspired by a tweet of
@gabrielpeyre
.
M1 and M2 are complex valued random matrices 500x500. How do eigenvalues of M1 (1-t) + M2 t move in ℂ when t ranges in [0,1]?
#mathart
#numpy
#python
#matplotlib
#python3
#math
#linearalgebra
6
49
389
I had never seen these fractals before, and they continue to amaze me.
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
15
44
391
Color version of "How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?"
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
2
62
397
A kissing Schottky group fractal. Circles in title.
Made with
#python
,
#matplotlib
and
#numpy
iterating circle inversions.
4
42
387
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
5
34
376
How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
5
51
376
5
37
365
Newton fractal created using the Newton method applied to a Blaschke product.
Made with
#Python
,
#Matplotlib
,
#NumPy
and
#Sympy
.
2
52
365
A contour plot depicting the absolute value of the numerical solution to the Feigenbaum-Cvitanović functional equation in the 3rd quadrant of complex plane.
A gem of chaos theory.
Made with
#python
,
#matplotlib
and
#numpy
.
8
36
341
1
35
351
Random fractal spirals generated by iterated function systems.
Made with
#python
,
#numpy
and
#matplotlib
4
59
342
A fractal flower generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below. Made with
#python
,
#matplotlib
and
#numpy
.
5
37
322
A symmetric attractors of a 𝑫ₙ equivariant map ℂ→ℂ. 𝑫ₙ is the group of symmetries of a regular polygon. In this case n=7.
The generic map is shown in the title of the figure.
Made with
#python
,
#matplotlib
and
#numpy
.
10
57
322
Ten million random walks on SL_2(ℤ) in the upper-half complex plane and then mapped to the unit disc by z→(z-i)/(z+i). Each walk starts from a point inside the fundamental domain of SL_2(ℤ).
Animated version.
Made with
#python
,
#matplotlib
and
#numpy
.
2
27
320
Fractals generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below. Made with
#python
,
#matplotlib
and
#numpy
.
6
35
319
Generated using the chaos game of the iterated function system defined by the maps ℂ→ℂ below.
Made with
#python
,
#matplotlib
and
#numpy
.
12
34
313
Color version of "How do the complex roots of the polynomial in the title move when t₁ and t₂ vary on S₁ x S₁?"
Made with
#python
,
#matplotlib
,
#numpy
and
#sympy
.
5
36
313
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
1
32
297
3
37
300
Relatives of the Koch curve with their similarity fractal dimensions calculated using Moran equation.
The original Koch curve is the one with d_s=1.26
Made with
#Python
,
#matplotlib
, and
#numpy
.
6
38
306