[Edu-sig] Brainstorming about January

[Gregor Lingl]

Kirby Urner schrieb:

>OK, ...
>
>===
>Math & Programming: From Chaos to Python
>
>Explore topics in mathematics by writing and modifying programs in a
>contemporary computer language.
>
Attention: this is a somewhat technical question/contribution (in 
contrast to the more philosophical ones concerning the design an 
didactics of cs courses)

Hi Kirby and all the others!

In one of my classes I'm just doing similar things. Starting with the 
very first program of John Zelle's  mervelous book I arrived at a 
program  drawing a Feigenbaum diagram.  With  this - and I think with 
all those  chaos/fractal-programs which use  pixel graphics - there  
occurs the problem, that  pixel graphics  with Tkinter  is *very* slow. 
Although I have used a few tricks to make the program fast it still 
needs approximately 50 seconds to draw the diagram (on my machine). 
Moreover it show's that the slow operation is indeed the put-method of 
PhotoImage (and the update method).  My students of course searching the 
net find Feigenbaum applets performing much faster. Being asked about 
that my (somewhat poor) answer is, yes it's slow in Python but the 
advantage is: *you* can write it in Python, whereas you can't write it 
in Java. Not really satisfying.
As this is a problem concerning a large class of applications (at least 
in the context of programming in highschool) I dream of having at hand 
some easily usable class which defines a window for doing fast pixel 
graphics.
As far as I know there are a *lot* of graphics-Toolkits for Python out 
there. Which of them could be used for this task? What are your 
experiences? Do you have significantly faster solutions?

Here is the code of my solution using Tkinter:

# Autor: Gregor Lingl
# Datum: 21. 10. 2004
# feigen.py : zeichnet ein Feigenbaum-Diagramm

from Tkinter import Tk, PhotoImage, Label

WIDTH = 700
HEIGHT = 500
NUM = 2*HEIGHT//3

def f(x):
    return LAMBDA * x * (1-x)

root = Tk()
root.title("Feigenbaum Diagram")
pic = PhotoImage(width=WIDTH+1, height=HEIGHT)
lbl = Label(root, image=pic, bg='white')
lbl.pack()

for i in range(8):
    for j in range(0,HEIGHT):
        pic.put("red", (int(round(WIDTH/7.0)*i),j))
root.update()

for frac in range(WIDTH):
    LAMBDA = 3.3 + frac*0.7/WIDTH
    x = 0.5   # initial value for iteration
    ys={}
    for i in range(150):
        x = f(x)
    for i in range(NUM):
        x = f(x)
        ys[int(HEIGHT*x)]=True
    for y in ys:
        pic.put("black", (frac,y))
    if frac%10==0:root.update()

root.mainloop()

>A goal of this class is to help you gain proficiency as a programmer, while
>delving into number theory, group theory, chaos and fractals, 
>
the above program was intended to do just this ...

Another example is from my book "Python für Kids" showing a more regular 
fractal (but suffering froom the same problem ...):

### Python für Kids - Kapitel 12 ###
# Autor: Gregor Lingl
# Datum: 13. 10. 2002
# simplefractal.py : zeichnet ein Sierpinsky-Dreieck

from Tkinter import Tk, PhotoImage, Label
from random import randrange, choice

def mittelpunkt(a,b):
    (x1,y1), (x2,y2) = a, b
    return ( int(round((x1+x2)/2.0)),
             int(round((y1+y2)/2.0)) )

def sierpinsky():
    global pixel
    while running:
        for i in range(20):
            ecke = choice(ecken)
            pixel = mittelpunkt(pixel,ecke)
            bild.put('black',pixel)
        root.update()

def start(event):
    print "START"
    global running
    running = 1
    sierpinsky()

def stop(event):
    print "STOP"
    global running
    running = 0

if __name__ == "__main__":
    root = Tk()
    bild = PhotoImage(width=300, height=300)
    lbl = Label(root, image=bild, bg='white')
    lbl.pack()
    root.bind('<Button-1>', start)
    root.bind('<Button-3>', stop)

    ecken = a, b, c = (20,265),(280,265),(150,40)
    pixel = randrange(300), randrange(300)
    for p in (a, b, c, pixel):
        bild.put("black", p)
    root.update()
    root.mainloop()


Any feedback, any suggestions, propositions, solutions are welcome

Regards,
Gregor

P.S.: Some conversations on the list - e. g. the one following the 
posting to which this is a reply - are really difficult to follow for 
me, as I'm not using English as a native language. Sometimes there seems 
to prevail some strange sort of humour or animosity. If that is funny 
for you, that's o.k. but nevertheless I doubt if it's useful for our 
concerns. (I'm well aware of the fact that it might be equally  
difficult for you to understand what I try to say in my rather poor 
English.)