@frederik
the solution of Fredrik is indeed megabit faster...
In the meantime (yesterday) I found another fix by using the python pillow environment. It works even faster than the solution of Frederic. Anyway it is strange that Drawbot does not offer a simple plot(x,y) statement

xscreen = 640
yscreen = 480
picname ="Feigenbaum.png"
newPage(xscreen,yscreen)

# Definitions for the pillow environment
import math
from PIL import Image, ImageDraw
colour = (255, 255, 255) #white
im = Image.new("RGB", (xscreen, yscreen), colour)
draw = ImageDraw.Draw(im)
# --------------------------------------

def f(p, k) :
    fwert = p + k * p * (1 - p)
    return fwert
 
def input():
    global left, right, bottom, top
    global invisible, visible
    left = 1.8
    right = 3.0
    bottom = 0.0
    top = 1.5
    invisible = 200
    visible = 200
    
def setup():
    input()
    feigenbaumIteration()
    # Show picture and save picture pillow environment
    im.show()
    im.save(picname)
            
def setglobalpoint(xw, yw):
    size = randint(1,1)
    middle = randint(-1,1)
    x = (xw - left) * xscreen / (right - left)
    y = (yw - bottom) * yscreen / (top - bottom)
    # point statement of pillow environment
    draw.point([(x, yscreen - y)], fill="black")
   
    
def feigenbaumIteration():
    deltaxPerPixel = (right - left) / xscreen
    for section in range(0, xscreen+1, 1):
        coupling = left + section * deltaxPerPixel
        population = 0.3
        for i in range(0, invisible+1, 1):
            population = f(population, coupling)
        for i in range(0, visible+1, 1):
            setglobalpoint(coupling, population)
            population = f(population, coupling)
            
    
setup()

@frederik
Works...
Great, thank you very much.
The only thing is that the computer graphics is shown on the screen, but the saved picture on the desktop is empty ?

Re: plot a single point how?

Hi Frederik, thank you for your clever idea! But sadly to say there is no speed improvement. It is as slow as the oval statement. It is difficult to understand that there is no dedicated command to draw a point. A picture with other python implementations like Thonney Python or Processing Python shows a picture at once.
So to speak it seems DrawBot is useless for making interesting Computer graphics pictures (Fractals for instance) without the usage of Turtle Graphics. Graphics in an x-y System needs two operations: to draw a point and to draw a line. What a pity that DrawBot is not able to do that ?
Here is the example with your proposal:
(As slow as the oval statement to draw a point)
Best regards (kalle)

xscreen = 640
yscreen = 480

newPage(xscreen,yscreen)

def f(p, k) :
    fwert = p + k * p * (1 - p)
    return fwert
 
def input():
    global left, right, bottom, top
    global invisible, visible
    left = 1.8
    right = 3.0
    bottom = 0.0
    top = 1.5
    invisible = 200
    visible = 200
    
def setup():
    input()
    feigenbaumIteration()
    saveImage("~/Desktop/feigenbaum.png")
        
def setglobalpoint(xw, yw):
    p = BezierPath()
    x = (xw - left) * xscreen / (right - left)
    y = (yw - bottom) * yscreen / (top - bottom)
    #oval(round(x),round(y),1,1)
    #these lines instead of command oval(round(x),round(y),1,1) 
    p.moveTo((x,y))
    p.lineTo((x,y))
    #strokeWidth(1)
    lineCap("round")
    stroke(0)
    drawPath(p)

    
def feigenbaumIteration():
    deltaxPerPixel = (right - left) / xscreen
    for section in range(0, xscreen+1, 1):
        coupling = left + section * deltaxPerPixel
        population = 0.3
        for i in range(0, invisible+1, 1):
            population = f(population, coupling)

        for i in range(0, visible+1, 1):
            setglobalpoint(coupling, population)
            population = f(population, coupling)
            
    
setup()

There is a line command to plot a line but no command to plot a point. Something like set point(x,y) is not available ? The workaround I use is the command for oval.
But the effect is that the drawing takes a lot of time...

some suggestion to improve would be helpful. EXAMPLE:

xscreen = 640
yscreen = 480

newPage(xscreen,yscreen)

def f(p, k) :
    fwert = p + k * p * (1 - p)
    return fwert
 
def input():
    global left, right, bottom, top
    global invisible, visible
    left = 1.8
    right = 3.0
    bottom = 0.0
    top = 1.5
    invisible = 200
    visible = 200
    
def setup():
    input()
    feigenbaumIteration()
    saveImage("~/Desktop/feigenbaum.png")
    
def setglobalpoint(xw, yw):
    x = (xw - left) * xscreen / (right - left)
    y = (yw - bottom) * yscreen / (top - bottom)
    oval(round(x),round(y),1,1)
    
def feigenbaumIteration():
    deltaxPerPixel = (right - left) / xscreen
    for section in range(0, xscreen+1, 1):
        coupling = left + section * deltaxPerPixel
        population = 0.3
        for i in range(0, invisible+1, 1):
            population = f(population, coupling)

        for i in range(0, visible+1, 1):
            setglobalpoint(coupling, population)
            population = f(population, coupling)
            
    
setup()