Differences between revisions 9 and 39 (spanning 30 versions)
⇤ ← Revision 9 as of 2009-05-21 20:58:19 →
Size: 7856
Editor: pang
Comment: Added "Queens on board"
← Revision 39 as of 2019-04-06 17:00:55 → ⇥
Size: 12801
Editor: chapoton
Comment:
Deletions are marked like this. Additions are marked like this.
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== Hearing a trigonometric identity ==
by Marshall Hampton. When the two frequencies are well separated, we hear the right hand side of the identity. When they start getting close, we hear the higher-pitched factor in the left-hand side modulated by the lower-pitched envelope.

{{{#!sagecell
import wave

class SoundFile:
   def __init__(self, signal,lab=''):
       self.file = wave.open('./test' + lab + '.wav', 'wb')
       self.signal = signal
       self.sr = 44100

   def write(self):
       self.file.setparams((1, 2, self.sr, 44100*4, 'NONE', 'noncompressed'))
       self.file.writeframes(self.signal)
       self.file.close()

mypi = float(pi)
from math import sin

@interact
def sinsound(freq_ratio = slider(1/144,1,1/144,1/12)):
    hz1 = 440.0
    hz2 = float(440.0*2^freq_ratio)
    html('$\cos(\omega t) - \cos(\omega_0 t) = 2 \sin(\\frac{\omega + \omega_0}{2}t) \sin(\\frac{\omega - \omega_0}{2}t)$')
    s2 = [sin(hz1*x*mypi*2)+sin(hz2*x*mypi*2) for x in srange(0,4,1/44100.0)]
    s2m = max(s2)
    s2f = [16384*x/s2m for x in s2]
    s2str = ''.join(wave.struct.pack('h',x) for x in s2f)
    lab="%1.2f"%float(freq_ratio)
    f = SoundFile(s2str,lab=lab)
    f.write()
    pnum = 1500+int(500/freq_ratio)
    show(list_plot(s2[0:pnum],plotjoined=True))
    html('<embed src="cell://test'+ lab +'.wav" width="200" height="100"></embed>')
    html('Frequencies: '+ '$\omega_0 = ' + str(hz1) + ' $, $\omega = '+latex(hz2) + '$')
}}}
{{attachment:sinsound.png}}

== Karplus-Strong algorithm for plucked and percussive sound generation ==
by Marshall Hampton

{{{#!sagecell
import wave

class SoundFile:
   def __init__(self, signal,lab=''):
       self.file = wave.open('./test' + lab + '.wav', 'wb')
       self.signal = signal
       self.sr = 44100

   def write(self):
       self.file.setparams((1, 2, self.sr, 44100*4, 'NONE', 'noncompressed'))
       self.file.writeframes(self.signal)
       self.file.close()

mypi = float(pi)
from math import sin

def ks(delay,length,blend = 0,filler=None,stretch=0):
    if filler == None:
        filler = [randint(-16383,16383) for q in range(delay+1)]
    outsig = filler[:]
    index = len(filler)
    while len(outsig) < length:
        s = random()
        if s > stretch:
            b = random()
            if b < 1-blend:
                newvalue = (outsig[index-delay]+outsig[index-delay-1])*.5
            else:
                newvalue = -(outsig[index-delay]+outsig[index-delay-1])*.5
        else:
            newvalue = outsig[index-delay]
        outsig.append(newvalue)
        index += 1
    return [int(round(x)) for x in outsig]

@interact
def sinsound(delay = slider([int(2^i) for i in range(2,10)], default=100, label="initial delay"), blend=slider(srange(0,1,.01,include_endpoint=True),default=0,label="blend factor"), stretch=slider(srange(0,1,.01,include_endpoint=True),default=0,label="stretch factor")):
    s2f = ks(delay,int(44100*(1/2)),blend=blend,stretch=stretch)
    for i in range(12):
        s2f = s2f + ks(int(2^((12+i)/12.0)*delay),int(44100*(1/2)),blend=blend, stretch=stretch)
    html("Karplus-Strong algorithm with blending and delay stretching")
    html("<br>K. Karplus and A. Strong, <em>Digital synthesis of plucked string and drum timbres</em>, \nComputer Music Journal 7 (2) (1983), 43–55.<br>")
    html("Initial waveform:")
    show(list_plot(s2f[0:2000],plotjoined=True), figsize = [7,3.5])
    html("Waveform after stabilization:")
    show(list_plot(s2f[20000:22000],plotjoined=True), figsize = [7,3.5])
    s2str = ''.join(wave.struct.pack('h',x) for x in s2f)
    lab=""
    f = SoundFile(s2str,lab=lab)
    f.write()
    html('<embed src="cell://test'+ lab +'.wav" width="200" height="100"></embed>')
}}}

{{attachment:KarplusStrong.png}}
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{{{ {{{#!sagecell
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    XY = X.intersection(Y)
    XZ = X.intersection(Z)
    YZ = Y.intersection(Z)
    XYZ = XY.intersection(Z)		     XY = X & Y
    XZ = X & Z
    YZ = Y & Z
    XYZ = XY & Z
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        Z = set(S[i]).intersection(S[(i+1)%3]).difference(set(XYZ))         Z = (set(S[i]) & S[(i+1)%3]) - set(XYZ)
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{{{ {{{#!sagecell
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{{{ {{{#!sagecell
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    print "<html>" # trick to avoid word wrap
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        cProfile.run(cmd)         cProfile.runctx(cmd,globals(), locals())
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        profile.run(cmd)
    print "</html>"		         profile.runctx(cmd,globals(), locals())
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{{{ {{{#!sagecell
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    print globals()[system].eval(code)     print(globals()[system].eval(code))
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== A Random Walk ==

by William Stein

{{{
html('<h1>A Random Walk</h1>')
vv = []; nn = 0
@interact
def foo(pts = checkbox(True, "Show points"),
        refresh = checkbox(False, "New random walk every time"),
        steps = (50,(10..500))):
    # We cache the walk in the global variable vv, so that
    # checking or unchecking the points checkbox doesn't change
    # the random walk.
    html("<h2>%s steps</h2>"%steps)
    global vv
    if refresh or len(vv) == 0:
        s = 0; v = [(0,0)]
        for i in range(steps):
             s += random() - 0.5
             v.append((i, s))
        vv = v
    elif len(vv) != steps:
        # Add or subtract some points
        s = vv[-1][1]; j = len(vv)
        for i in range(steps - len(vv)):
            s += random() - 0.5
            vv.append((i+j,s))
        v = vv[:steps]
    else:
        v = vv
    L = line(v, rgbcolor='#4a8de2')
    if pts: L += points(v, pointsize=10, rgbcolor='red')
    show(L, xmin=0, figsize=[8,3])
}}}
{{attachment:randomwalk.png}}

== 3D Random Walk ==
{{{
@interact
def rwalk3d(n=(50,1000), frame=True):
    pnt = [0,0,0]
    v = [copy(pnt)]
    for i in range(n):
        pnt[0] += random()-0.5
        pnt[1] += random()-0.5
        pnt[2] += random()-0.5
        v.append(copy(pnt))
    show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame)
}}}
{{attachment:randomwalk3d.png}}
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{{{
def minkdemo(list1,list2):		 {{{#!sagecell
def minkdemo(list1, list2):
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    Returns the Minkowski sum of two lists.     Return the Minkowski sum of two lists.
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            temp = [stuff1[i] + stuff2[i] for i in range(len(stuff1))]
            output.append(temp)		             output.append([a + b for a, b in zip(stuff1, stuff2)])
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@interact
def minksumvis(x1tri = slider(-1,1,1/10,0, label = 'Triangle point x coord.'), yb = slider(1,4,1/10,2, label = 'Blue point y coord.')):
    t_list = [[1,0],[x1tri,1],[0,0]]
@interact
def minksumvis(x1tri=slider(-1,1,1/10,0, label='Triangle point x coord.'), yb=slider(1,4,1/10,2, label='Blue point y coord.')):
    t_list = [[1,0], [x1tri,1], [0,0]]
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    for an_edge in p12poly.vertex_adjacencies():
        edge_lines = edge_lines + line([verts[an_edge[0]], verts[an_edge[1][0]]])
        edge_lines = edge_lines + line([verts[an_edge[0]], verts[an_edge[1][1]]])		     for v0, v1 in p12poly.graph().edges(False):
       edge_lines += line([v0, v1])
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        triangle_sum = triangle_sum + polygon(temp_list, alpha = .5, rgbcolor = (1,0,0))         triangle_sum += polygon(temp_list, alpha = .5, rgbcolor = (1,0,0))
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        kite_sum = kite_sum + polygon(temp_list, alpha = .3,rgbcolor = (0,0,1))         kite_sum += polygon(temp_list, alpha = .3,rgbcolor = (0,0,1))
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    labels = labels + text('=', (-.2,.5), rgbcolor = (0,0,0))     labels += text('=', (-.2,.5), rgbcolor = (0,0,0))
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== Queens on board ==
An interaction to play with the problem of placing eight queens on a board so that they do not threaten each other. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3.
by Pablo Angulo
{{{
queens=[]
opciones=['Clean board', 'Add queen', 'Remove queen' ]

@interact
def _(queen=input_box(default=(0,0)), opcion=selector(opciones, buttons=True), auto_update=False ):
    global queens
    if opcion=='Clean board':
        queens=[]
    elif opcion=='Add queen':
        if queen not in queens:
            queens.append(queen)
== Cellular Automata ==
by Pablo Angulo, Eviatar Bach

{{{#!sagecell
from numpy import zeros
from random import randint

def cellular(rule, N, initial='Single-cell'):
    '''Yields a matrix showing the evolution of a Wolfram's cellular automaton
    
    rule: determines how a cell's value is updated, depending on its neighbors
    N: number of iterations
    initial: starting condition; can be either single-cell or a random binary row
    '''
    M=zeros( (N,2*N+2), dtype=int)
    if initial=='Single-cell':
        M[0,N]=1
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        queens.remove(queen)
        
    board=matrix(ZZ,8,8)
    for x in range(8):
        for y in range(8):
            board[x,y]=(x+y)%2*7
    for x,y in queens:
        for i in range(8):
            if i!=y: board[x,i]=1+(x+i)%2*5
            if i!=x: board[i,y]=1+(i+y)%2*5
        for i in range(-min(x,y),min(8-x,8-y)):
            if i!=0: board[x+i,y+i]=1+(x+y)%2*5
        for i in range(max(-x,y-7),min(8-x,y+1)):
            if i!=0: board[x+i,y-i]=1+(x+y)%2*5
    for x,y in queens:
        if ( board[x,y]==1 or board[x,y]==6 ):
            print 'Queen at (%d,%d) is threatened by another queen'%(x,y)
            board[x,y]=4
        else:
            board[x,y]=3
    show(matrix_plot(board, cmap='Oranges' ))		         M[0]=[randint(0,1) for a in range(0,2*N+2)]
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}}}
{{attachment:queens.png}}		     for j in range(1,N):
        for k in range(0,2*N):
            l = 4*M[j-1,k-1] + 2*M[j-1,k] + M[j-1,k+1]
            M[j,k]=rule[ l ]
    return M[:,:-1]
    
def num2rule(number):
    if not 0 <= number <= 255:
        raise Exception('Invalid rule number')
    binary_digits = number.digits(base=2)
    return binary_digits + [0]*(8-len(binary_digits))

@interact
def _( initial=selector(['Single-cell', 'Random'], label='Starting condition'), N=input_box(label='Number of iterations',default=100),
       rule_number=input_box(label='Rule number',default=110),
       size = slider(1, 11, label= 'Size', step_size=1, default=6 ), auto_update=False):
    rule = num2rule(rule_number)
    M = cellular(rule, N, initial)
    plot_M = matrix_plot(M, cmap='binary')
    plot_M.show( figsize=[size,size])
}}}
{{attachment:cellular2.png}}

== Another Interactive Venn Diagram ==
by Jane Long (adapted from http://wiki.sagemath.org/interact/misc)

This interact models a problem in which a certain number of people are surveyed to see if they participate in three different activities (running, biking, and swimming). Users can indicate the numbers of people in each category, from 0 to 100. Returns a graphic of a labeled Venn diagram with the number of people in each region. Returns an explanatory error message if user input is inconsistent.

{{{#!sagecell
@interact
def _(T=slider([0..100],default=100,label='People surveyed'),X=slider([0..100],default=28,label='Run'), Y=slider([0..100],default=33,label='Bike'), Z=slider([0..100],default=59,label='Swim'),XY=slider([0..100],default=16,label='Run and Bike'),XZ=slider([0..100],default=13,label='Run and Swim'),YZ=slider([0..100],default=12,label='Bike and Swim'),XYZ=slider([0..100],default=7,label='Run, Bike, and Swim')):
   
    centers = [(cos(n*2*pi/3), sin(n*2*pi/3)) for n in [0,1,2]]
    scale = 1.7
    clr = ['yellow', 'blue', 'green']
    G = Graphics()
    for i in range(3):
        G += circle(centers[i], scale, rgbcolor=clr[i],
             fill=True, alpha=0.3)
    for i in range(3):
        G += circle(centers[i], scale, rgbcolor='black')
   
    # Label sets
    G += text('Run',(3,0),rgbcolor='black')
    G += text('Bike',(-1,3),rgbcolor='black')
    G += text('Swim',(-1,-3),rgbcolor='black')
   
    # Plot pairs of intersections
    ZX=XZ-XYZ
    G += text(ZX, (1.3*cos(2*2*pi/3 + pi/3), 1.3*sin(2*2*pi/3 + pi/3)), rgbcolor='black')
    YX=XY-XYZ
    G += text(YX, (1.3*cos(0*2*pi/3 + pi/3), 1.3*sin(0*2*pi/3 + pi/3)), rgbcolor='black')
    ZY=YZ-XYZ
    G += text(ZY, (1.3*cos(1*2*pi/3 + pi/3), 1.3*sin(1*2*pi/3 + pi/3)), rgbcolor='black')
  
    # Plot what is in one but neither other
    XX=X-ZX-YX-XYZ
    G += text(XX, (1.5*centers[0][0],1.7*centers[0][1]), rgbcolor='black')
    YY=Y-ZY-YX-XYZ
    G += text(YY, (1.5*centers[1][0],1.7*centers[1][1]), rgbcolor='black')
    ZZ=Z-ZY-ZX-XYZ
    G += text(ZZ, (1.5*centers[2][0],1.7*centers[2][1]), rgbcolor='black')
 
    # Plot intersection of all three
    G += text(XYZ, (0,0), rgbcolor='black')
   
    # Indicate number not in X, in Y, or in Z
    C = T-XX-YY-ZZ-ZX-ZY-YX-XYZ
    G += text(C,(3,-3),rgbcolor='black')
    
    # Check reasonableness before displaying result
    if XYZ>XY or XYZ>XZ or XYZ>YZ or XY>X or XY>Y or XZ>X or XZ>Z or YZ>Y or YZ>Z or C<0 or XYZ<0 or XZ<0 or YZ<0 or XY<0 or X<0 or Y<0 or Z<0:
        print('This situation is impossible! (Why?)')
    else:
        G.show(aspect_ratio=1, axes=False)
}}}
{{attachment:vennjhl.png}}

Sage Interactions - Miscellaneous

goto interact main page

Contents

  1. Sage Interactions - Miscellaneous
    1. Hearing a trigonometric identity
    2. Karplus-Strong algorithm for plucked and percussive sound generation
    3. An Interactive Venn Diagram
    4. Unreadable code
    5. Profile a snippet of code
      1. Evaluate a bit of code in a given system
    6. Minkowski Sum
    7. Cellular Automata
    8. Another Interactive Venn Diagram

Hearing a trigonometric identity

by Marshall Hampton. When the two frequencies are well separated, we hear the right hand side of the identity. When they start getting close, we hear the higher-pitched factor in the left-hand side modulated by the lower-pitched envelope.

sinsound.png

Karplus-Strong algorithm for plucked and percussive sound generation

by Marshall Hampton

KarplusStrong.png

An Interactive Venn Diagram

veng.png

Unreadable code

by Igor Tolkov

unreadable.png

Profile a snippet of code

profile.png

Evaluate a bit of code in a given system

by William Stein (there is no way yet to make the text box big):

evalsys.png

Minkowski Sum

by Marshall Hampton

minksum.png

Cellular Automata

by Pablo Angulo, Eviatar Bach

cellular2.png

Another Interactive Venn Diagram

by Jane Long (adapted from http://wiki.sagemath.org/interact/misc)

This interact models a problem in which a certain number of people are surveyed to see if they participate in three different activities (running, biking, and swimming). Users can indicate the numbers of people in each category, from 0 to 100. Returns a graphic of a labeled Venn diagram with the number of people in each region. Returns an explanatory error message if user input is inconsistent.

vennjhl.png

interact/misc (last edited 2020-06-05 20:32:41 by mathzeta2)