𝜋 Approximation

2015-12-19, post № 91

mathematics, programming, Python, #approximating, #approximation, #circle, #circle constant, #constant, #Euler, #infinite, #infinite sum, #pi, #sum

Using an infinite series shown by Euler, 𝜋 can be approximated.
The series goes as follows: $\sum\limits_{n=1}^{\infty}\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\dots=\frac{\pi^2}{6}$
By rearranging the equation, you get the following: $\pi=\sqrt{6\cdot\big(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\dots\big)}$

Source code: pi-approximation.py

Third Sunday in Advent

2015-12-13, post № 90

art, #Advent, #animated, #animated gif, #animation, #gif, #pixel candle, #pixel guy, #third, #third candle, #third Sunday, #third Sunday in Advent, #third Sunday of Advent

Lighting the third candle…

Mandelbrot Set

2015-12-12, post № 89

mathematics, programming, Pygame, Python, #colorful, #complex, #fractal, #f_c(z) = z^2 + c, #imaginary, #iterating, #iteration, #Mandelbrot, #repeating, #self-repeathing, #set

Working with complex numbers and iterating the function $f_c(z)=z^2+c$ , I created this program which lets you explore the depth of this self-repeating fractal. The different colors are caused by different color schemes.

Controls

Left mouse click and mouse movements control the zoom frame,
Middle mouse click zooms in,
‘Space’ takes a screenshot,
‘F1’ moves a zoom back,
‘F2’ zooms to default zoom.

mandelbrot-set-188_-6.75_-4.5_6.75_4.5.png

mandelbrot-set-181_-0.17466172461436666_-1.0720840874732396_-0.1746617232046618_-1.0720840865334365.png

mandelbrot-set-142_-0.16101577503429365_-1.0369693644261544_-0.16019958847736634_-1.0364252400548697.png

mandelbrot-set-124_0.25_-0.04999999999999982_0.40000000000000036_0.04999999999999982.png

mandelbrot-set-052_0.18276898469650216_-0.5821251321730682_0.18311316336591232_-0.5818956797267948.png

Source code: mandelbrot-set.py

Second Sunday in Advent

2015-12-06, post № 88

art, #Advent, #animated, #animated gif, #animation, #candle, #gif, #pixel candle, #pixel guy, #second, #second Advent, #second candle, #second Sunday, #second Sunday in Advent, #second Sunday of Advent, #Sunday

Lighting the second candle…

c’t Racetrack II

2015-12-05, post № 87

games, programming, Pygame, Python, #advanced, #c't, #c't-Racetrack, #car, #car race, #race, #racetrack, #vertrac't

Since the 30th of November 2015 the contest is over. The code is now visible in my post c’t-Racetrack. In this time I improved my program and added a semi-working collision detection (unfortunately it does not cover every case), a helper function (will not allow you to make an invalid move) and an additional view mode (lets you only see the car’s path).

Controls

Mouse movement changes the new acceleration vector applied in the next step,
Left click moves one step,
Right click is a undo for the latest move,
Middle click moves the frame,
‘F1’ toggles view mode,
‘F2’ takes a screenshot,
‘F3’ exports current moves,
‘F4’ resets the game,
‘h’ toggles helper.

Source code: ct-racetrack-ii.py

First Sunday in Advent

2015-11-29, post № 86

art, #Advent, #animated, #animated gif, #candle, #first, #first Advent, #first candle, #first of Advent, #first Sunday, #first Sunday in Advent, #first Sunday of Advent, #gif, #pixel, #pixel candle, #pixel guy, #Sunday

Lighting the first candle…

Extra assets: first-sunday-in-advent_spacing.txt

Sleeper

2015-11-28, post № 85

programming, Python, #sleep, #snore, #time, #time.sleep(), #z

Taking time.sleep() to the next level.

Source code: sleeper.py

Bubbles

2015-11-22, post № 84

programming, Pygame, Python, #background, #bubbles, #color, #gfx, #pygame.gfxdraw()

Playing around with pygame.gfxdraw(), I created this program, which just draws some bubbles on the screen.