# This snippet can be used to play with 2d IFSs# The next three lines will allow us to use the relevant functions down below# and to make sure that we are starting with a clean slate. You dont really# have to worry about them, just make sure you run them at the start. Dont worry# about any warnings.restart;with(plots,display):with(linalg):# This procedure defines our IFS. The point passed in is a vector of 2 reals# and each element is accessed by point[1] and point[2]. The map parameter should# vary from 1 to the number of maps. Each of the if statements defines a map and# to add more simiply follow the format that is already thereifs := proc(point,map)
local retpt:
# This is the start of the maps
if (map = 1)
then
retpt := evalm([[1,0],[0,0.5]] &* point + [0,0.5]):
fi:
if (map = 2)
then
retpt := evalm([[0.5,0.5],[-0.4,0.5]] &* point + [0.2,0.5]):
fi:
if (map = 3)
then
retpt := evalm([[-0.4,0],[0,0.5]] &* point + [-0.5,0.5]):
fi:
# This is the end of the maps
return([retpt[1],retpt[2]]):
end:# This is just an easy way to get a random integer between 1 and 3. Hit return# a couple of times on themap(); and you will see it returning random integers in# that range. To change the range simply change the 3themap := rand(1..3):themap();# This is the nuts and bolts of what we are doing. We are tracking the points we# have visited so far with points1 (the first line empties the list) and we are# starting at startpt (which we initialise to [0,0]).# The first for loop just randomly iterates 20 times and does not store the result,# this is to move us close to the attractor (if we are not already on it).# The second for loop does 500 more iterations - but this time we remember the# points we hit (in the middle of the three indented lines).points1 := []:
startpt := [0,0]:
for i from 1 to 20 do
nextpt := evalm(ifs(startpt,themap())):
startpt := evalm(nextpt):
od:
for i from 1 to 500 do
nextpt := evalm(ifs(startpt,themap())):
points1 := [op(points1), [evalm(nextpt)[1], evalm(nextpt)[2]]]:
startpt := evalm(nextpt):
od:# Here is where we actually display the list of points that we have generatedplot1 := plot(points1, style=POINT,colour=BLACK,symbol=POINT,axes=NONE):display(plot1);