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
.
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
.
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
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
.
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below.
Made with
#python
,
#matplotlib
and
#numpy
.
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:
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
.
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
.
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
.
Fractals generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
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
.
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
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
.
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
.
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
.
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
.
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
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
.
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
.
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
.
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
.
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
.
Fractal generated using the chaos game of the iterated function system defined by the Möbius transformations below. Made with
#python
,
#matplotlib
and
#numpy
.
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
.