Is it possible do this processing.gif in drawbot?

That would be really cool if dooable.
 I would start with a single element, with the movement.
 six points as the blue hexagon, they keep position but change from corner to round
 six points as the pink circle, with changing positions
 questions:
curveTo() or path.curveTo()?
how can I do the math for a) the positionchange and b) for the bezierhandleschange? with trigonomety, or would I need pi?
 I would do a grid. I'm familiar with a sqare kind of grid. In this case it should be radial. I have no idea how to do this...
As you see, I'm quite at the beginning

 Without doing too much math, and using some ugly constants, you can draw a segment of the hexagon.
Draw and rotate it six times, and you have the basis of the hexagon.
def draw_segment(): # Coordinates based on a circle with diameter 1000 and center at 0,0 first_point = (500, 0) first_control_point = (500, 185.191467285156) second_control_point = (399.316345214836, 346.863525390625) second_point = (249.704528808587, 433.274108886719) # Make and draw path bez = BezierPath() bez.moveTo(first_point) bez.curveTo(first_control_point, second_control_point, second_point) drawPath(bez) def draw_hexagon(): for i in range(6): with savedState(): translate(500,500) scale(0.5, 0.5) rotate(i * 60, center=(0, 0)) draw_segment() newPage() fill(None) stroke(0) strokeWidth(10) draw_hexagon()

 Changing the bezierhandle is a simple as calculating a point between two extremes, based on a percentage, based on how far you are in your animation.
(Check out easings.net to create smoother animations)
frames = 12 def draw_segment(percentage): first_point = (500, 0) first_control_point_convex = (500, 185.191467285156) first_control_point_concave = (350.388183585986, 86.410583482659) second_control_point_convex = (399.316345214836, 346.863525390625) second_control_point_concave = (249.704528786313,248.082641579087) second_point = (249.704528808587, 433.274108886719) # Calculate inbetween points based on percentage fcpcx = first_control_point_convex[0] + percentage * (first_control_point_concave[0]  first_control_point_convex[0]) fcpcy = first_control_point_convex[1] + percentage * (first_control_point_concave[1]  first_control_point_convex[1]) scpcx = second_control_point_convex[0] + percentage * (second_control_point_concave[0]  second_control_point_convex[0]) scpcy = second_control_point_convex[1] + percentage * (second_control_point_concave[1]  second_control_point_convex[1]) first_control_point = (fcpcx, fcpcy) second_control_point = (scpcx, scpcy) # Make and draw path bez = BezierPath() bez.moveTo(first_point) bez.curveTo(first_control_point, second_control_point, second_point) drawPath(bez) def draw_hexagon(percentage): for i in range(6): with savedState(): translate(500,500) scale(0.5, 0.5) rotate(i * 60, center=(0, 0)) draw_segment(percentage) for i in range(frames): newPage() fill(None) stroke(0) strokeWidth(10) percentage = i / frames draw_hexagon(percentage) for i in range(frames, 0, 1): newPage() fill(None) stroke(0) strokeWidth(10) percentage = i / frames draw_hexagon(percentage) saveImage("animated.gif")

 I donβt think you need a radial grid.
If you base the timing of the animation of one hexagon on its distance to the center point, I believe you get the same effect as in your example.

an other solution!
# amount of corners, 6 will create a hexagon corners = 6 # the radius of the circle radius = 100 # amount of frames frames = 24 # calculate the step in radians of each corner angleStep = pi * 2 / corners # calculate the distance between each point on the circle # based on the cos, sin of the angle the opposite 'c' can be # calculated with pythagoras distance = sqrt((radius  cos(angleStep) * radius) ** 2 + (sin(angleStep) * radius) ** 2) # calculate the offcurve handle length offCurveLength = distance * 0.38 # the extremes of factors we would like to use minFactor = .3 maxFactor = 2 # start the loop for i in range(frames): # calculate a factor and normalize so it goes from 0 > 1 > 0 # to create a loop factor = i / (frames) * 2 if factor > 1: factor = 2  factor # interpolate the factor with our min max settings factor = minFactor + (maxFactor  minFactor) * factor # create a new page newPage(radius * 4, radius * 4) # draw a white background (gifs dont have an alpha value) with savedState(): fill(1) rect(0, 0, width(), height()) # translate to the middle translate(width() / 2, height() / 2) # create a pen pen = BezierPath() # use the pen as a point pen # so we can just add point instead of segments pen.beginPath() # start a loop over all corners for i in range(corners): # get the angle of each corner angle = angleStep * i # get the x, y position based on the angle and radius x = cos(angle) * radius y = sin(angle) * radius # get the off curces based on the hooked angle (+90Β°) # and multiply by the factor offx1 = (x + cos(angle + pi / 2) * offCurveLength) * factor offy1 = (y + sin(angle + pi / 2) * offCurveLength) * factor offx2 = (x  cos(angle + pi / 2) * offCurveLength) * factor offy2 = (y  sin(angle + pi / 2) * offCurveLength) * factor # add the point to the point pen path pen.addPoint((offx2, offy2)) pen.addPoint((x, y), segmentType="curve") pen.addPoint((offx1, offy1)) # tell the path the drawing is done pen.endPath() # draw the path stroke(1, 0, 1, 1) strokeWidth(10) fill(None) drawPath(pen) # save the gif saveImage("circleHex.gif")

A simple example of how to move the wave through a grid of dots. The position of the dots does not matter.
@frederik probably has a better and more robust solution for this also

frames = 24 page_size = 1000 grid_size = 20 grid_spacing = page_size / grid_size min_dot_size = 10 max_dot_size = 50 radius = 100 def draw_dot(center, diameter): x = center[0]  diameter / 2 y = center[1]  diameter / 2 oval(x, y, diameter, diameter) for f in range(frames): percentage_animated = f / frames newPage() fill(0) rect(0, 0, page_size, page_size) for row in range(grid_size): for column in range(grid_size): x = row * grid_spacing + grid_spacing / 2 y = column * grid_spacing + grid_spacing / 2 # Calculate distance from (x,y) of the dot to the center of the page distance = pow( (pow(x  page_size / 2, 2 ) + pow(y  page_size / 2, 2)), 0.5) # The wave must seem to move, so for every frame in the # animation, add a precentage of the length of the wave. # Add or substract to change direction. distance = distance  percentage_animated * radius * 2 # Use modulo to get a distance between 0 and double the radius distance = distance % (radius * 2) # The wave has a lenghth of double the radius. In the # first halve of the lenght, the dots get larger, in the # second halve the dots get smaller. # So, we calculate a percentage between 0 and 2, and when # the percentage is larger than 1, we count backwards. percentage = distance / radius if percentage > 1: percentage = 2  percentage dot_size = min_dot_size + percentage * (max_dot_size  min_dot_size) fill(1) draw_dot((x,y), dot_size) saveImage("animated.gif")

Almost the same code, but instead of drawing a grid we draw 1000 circles randomly. As they have to stay in the same place, we save their locations in an array.
(Also in this script some nice code to have if you want to publish animated gifs; a way to reduce the colours in the gif.)
import random import struct frames = 24 page_size = 1000 number_of_circles = 1000 min_dot_size = 10 max_dot_size = 70 radius = 200 # create color table for gif # https://stackoverflow.com/questions/6269765/whatdoesthebcharacterdoinfrontofastringliteral table = b"" greys = [0,85,170,255] for i in greys: r = struct.pack(">B", i) g = struct.pack(">B", i) b = struct.pack(">B", i) table += r + g + b # + a def draw_dot(center, diameter): x = center[0]  diameter / 2 y = center[1]  diameter / 2 oval(x, y, diameter, diameter) # Generate circles, randomly distributed circles = [] for i in range(number_of_circles): x = random.randint(0,page_size) y = random.randint(0,page_size) circles.append((x,y)) for f in range(frames): percentage_animated = f / frames newPage() fill(0) rect(0, 0, page_size, page_size) for c in circles: x = c[0] y = c[1] distance = pow( (pow(x  page_size / 2, 2 ) + pow(y  page_size / 2, 2)), 0.5) distance = distance  percentage_animated * radius * 2 distance = distance % (radius * 2) percentage = distance / radius if percentage > 1: percentage = 2  percentage dot_size = min_dot_size + percentage * (max_dot_size  min_dot_size) fill(None) stroke(1) draw_dot((x,y), dot_size) saveImage("animated.gif", imageGIFRGBColorTable = table)

@monomonnik
How could you figure out the controlpoints and the second point for the segment (your first code snippet)?
(My "solution" would be, draw it in illustrator at the right coordinates, and copy/paste the numbers to drawbot.)

It's fantastic, what is possible in drawbot!
Thank you @monomonnik for your great help!
Also @frederik for other interesting solutions! Thank you bothSome really new topics to me, and I need some time to understand step by (small) step.

@pi That is exactly my solution. Itβs not elegant, but itβs quick and it works.
Below is the Applescript I used. If you name your paths in Illustrator and put the names in pathNames it will copy the coordinates of the points and corresponding control points to an array you can paste in DrawBot.
on run set pathNames to {"segment_concave"} set pathsArray to "segment = [" tell application "Adobe Illustrator" activate set docRef to current document repeat with pathName in pathNames set pointsArray to "[" set itemRef to path item pathName of docRef set pointsRef to every path point of itemRef repeat with pointRef in pointsRef  anchor point set pointAsString to "[" set x to my string_float(item 1 of anchor of pointRef) set y to my string_float(item 2 of anchor of pointRef) set pointAsString to pointAsString & "(" & x & "," & y & "), "  left bcp set x to my string_float(item 1 of left direction of pointRef) set y to my string_float(item 2 of left direction of pointRef) set pointAsString to pointAsString & "(" & x & "," & y & "), "  right bcp set x to my string_float(item 1 of right direction of pointRef) set y to my string_float(item 2 of right direction of pointRef) set pointAsString to pointAsString & "(" & x & "," & y & ")" set pointAsString to pointAsString & "]" set pointsArray to pointsArray & pointAsString & ", " end repeat set pointsArrayLength to length of pointsArray set pointsArray to (characters 1 through (pointsArrayLength  2) of pointsArray) as string set pointsArray to pointsArray & "]" set pathsArray to pathsArray & pointsArray & ", " end repeat set pathsArrayLength to length of pathsArray set pathsArray to (characters 1 through (pathsArrayLength  2) of pathsArray) as string set pathsArray to pathsArray & "]" end tell activate set the clipboard to pathsArray log pathsArray end run on string_float(s) set s to s as string set new_s to "" repeat with c in s if c as string is equal to "," then set c to "." set new_s to new_s & c as string end repeat return new_s end string_float

@frederik: Why is it 0.38?
# calculate the offcurve handle length offCurveLength = distance * 0.38
Still a few things I don't understand so far.
And I didn't find out, how to have one color for the circle, and a second color for the star.BUT IT WORKS, thanks to all your inputs!
And it's fun to figure things out (if there's no deadline ).
This is my result (probably not with a very clean code...):frames = 36 ## circleHex corners = 6 radius_hex = 3*8 angleStep = pi * 2 / corners # = 1.0471975511965976 distance_hex = sqrt((radius_hex  cos(angleStep)*radius_hex) **2 + (sin(angleStep)*radius_hex) **2) # =radius_hex offCurveLength = distance_hex * 0.38 minFactor = .6 maxFactor = 1 grid_spacingX = radius_hex/3 * 4 # 32 grid_spacingY = 28 # radius_hex/3 * 4  4 > doesn's work stepsX = 27 stepsY = 15 pageW = 24*grid_spacingX + 2*radius_hex # 816 pageH = 14*grid_spacingY + 2*radius_hex # 440 radius_wave = pageW/4 for f in range(frames): newPage(pageW, pageH) fill(0) rect(0, 0, pageW, pageH) ## circleHex factor = f / frames * 2 if factor > 1: factor = 2  factor percentage_animated = f / frames for row in range(stepsX): for column in range(stepsY): x = row * grid_spacingX y = column * grid_spacingY # Calculate distance from (x,y) of each circleHex to the center of the page distance = pow( (pow(x  pageW/2, 2 ) + pow(y  pageH/2 + grid_spacingY, 2)), 0.5) # The wave must seem to move, so for every frame in the # animation, add a precentage of the length of the wave. # Add or substract to change direction. distance = distance  percentage_animated * radius_wave * 2 # Use modulo to get a distance between 0 and double the radius distance = distance % (radius_wave * 2) # The wave has a lenghth of double the radius. In the # first halve of the lenght, the dots get larger, in the # second halve the dots get smaller. # So, we calculate a percentage between 0 and 2, and when # the percentage is larger than 1, we count backwards. percentage = distance / radius_wave if percentage > 1: percentage = 2  percentage # interpolate the factor with our min max settings factor = minFactor + percentage * (maxFactor  minFactor) blendMode("hardLight") fill(0.8,0,0.8, .3) strokeWidth(None) with savedState(): if y in range(0, pageH, grid_spacingY*2): print(y) pen = BezierPath() pen.beginPath() translate(x + radius_hex  grid_spacingX/2, y + radius_hex) for i in range(corners): angle = angleStep * i x = cos(angle) * radius_hex y = sin(angle) * radius_hex offx1 = (x + cos(angle + pi / 2) * offCurveLength) * factor offy1 = (y + sin(angle + pi / 2) * offCurveLength) * factor offx2 = (x  cos(angle + pi / 2) * offCurveLength) * factor offy2 = (y  sin(angle + pi / 2) * offCurveLength) * factor pen.addPoint((offx2, offy2)) pen.addPoint((x, y), segmentType="curve") pen.addPoint((offx1, offy1)) pen.endPath() drawPath(pen) else: pen = BezierPath() pen.beginPath() translate(x + radius_hex  grid_spacingX, y + radius_hex) for i in range(corners): angle = angleStep * i x = cos(angle) * radius_hex y = sin(angle) * radius_hex offx1 = (x + cos(angle + pi / 2) * offCurveLength) * factor offy1 = (y + sin(angle + pi / 2) * offCurveLength) * factor offx2 = (x  cos(angle + pi / 2) * offCurveLength) * factor offy2 = (y  sin(angle + pi / 2) * offCurveLength) * factor pen.addPoint((offx2, offy2)) pen.addPoint((x, y), segmentType="curve") pen.addPoint((offx1, offy1)) pen.endPath() drawPath(pen)


@pi said in Is it possible do this processing.gif in drawbot?:
@frederik: Why is it 0.38?
the handle of the off curve is 38% of the distance between the oncurve points, that seems to be generating nice curves

@frederik
Cool, thanks  less math, more trying out