so here is a website that i have openedits
a it has a very nice animation of the conceptits
by frank mccown as you can seeit there is
a beautiful description of the model and a
very nice simulation of the modulus by if
you can see in the acknowledgement in fact
thein the creator of this simulation acknowledges
the text book that we have we are using for
thecourse network stores in markets all right
so here is thesimulation facility let me hit
the reset button and as you would have guessed
that red and blue here denote two different
types of people who have populated this city
and white represents blank where anybody can
shift so here have some parameter which are
againwhich are again quite self explanatory
all though i will try explaining them for
you
so this is this time for how similar do you
expect the how how similar do each node expect
their neighbours if i put twenty five percent
here it is the t value that i explained just
now the t value i say t equals three if its
twenty five percent i am surrounded by as
you know eight people twenty percent of eight
people is how mucheight into one by four which
is two so if any person has two neighbours
of the same colour then he is deemed to be
happy and satisfied he will not shift and
anyone who is not surrounded byat least two
people of the same colour that person will
try to shift to a blank space ok and the rest
is the distribution of red and blue it's the
same when i say fifty fifty you can in fact
change it empty space i have kept some ten
percent you can in fact change this two size
is a fifty ka fifty grid delay is the delay
between two steps of the animation i have
kept its zero
so let me reset it once again and then let
me start the simulation as i start you will
see that the number of people who are satisfied
will be displayed here as of now nobody is
satisfied it says zero percent people are
satisfied which means nobody is surrounded
byat least twenty five percent ofpeople who
are happy now basically once you start the
animation only this will start counting as
you can see i hit the start button and you
see hundred percent people are satisfied it
took just eight rounds as you can see every
single person is surrounded by at least two
neighbours of its type thats the similarity
percentage that i gave t equals basically
two now it will make t equals four which is
fifty percent out of eight people who my know
i would expect half of them to be of my type
if the reset and then start the simulation
and see the beautiful convergence of segregation
that happens here right now
I hit the start button now please observe
look at this they are getting segregated and
you see there is some beautiful segregation
happening here right then you expect half
the people to be of your type you observe
segregation happening right let me try increasing
it all the more reset and increase this to
lets say seventy five percent what you expect
now whether lets pause for a minute and then
see what what what i am doing here i am saying
seventy five percent of my neighbourhood should
be of my type which means if you take a blue
redah cell herei should have at least more
than what is seventy five percent of eight
neighbours it is six this red person should
have six people surrounding him only then
he is redeemed happy otherwise you would want
to shift which means as you can see none of
them are happy here right let me start the
simulation and see what happens see they are
now moving moving to the empty spacesnow roughly
if fifty percent of the people are happy and
then it goes on and on look at the beautiful
segregation that's happening
see more and more people get segregated and
there are clusters that are emerging you see
of huge blue cluster here and a red cluster
here and you see eighty percent people are
happy you see the stick more and more correct
you see that is the segregation is beautifully
going towards hundred percent now very soon
you will see all of them are actually happy
as you can see the number of rounds here in
this case when similarity percentage is high
when t is high seems to take a lot of time
you see the some problem in the boundary now
with converges beautifully you see there is
basically simply three clusters cluster one
i am sorry four clusters cluster one cluster
two cluster three and cluster four of course
you have clusters here as well butah i think
we can ignore it right
so basically there are four big clusters so
the simulation says that more the similarity
that you expect e better is the segregation
if you actually i I am sure you would know
what we we can guess what will happen if i
make it eighty nine percent it will probably
take a long time but let's see what happens
from here you see you see the people become
lessand less satisfied because eighty nine
percent is what it is not achievable as you
knoweighty nine percent ismore than seven
people should be of your type i mean that's
not possible right not even more than seven
almost almost eight people all your neighbour
should be of your type thats not possible
so it is a sort of simulation gets confused
this might even go forever
so if you sort of reduce it you will observe
that the convergence happens very quickly
reset start for thirty percent which very
quick yeah thanks to the create of this simulationwe
can explain this very easily with the simulation
thanah verbal explanation also it is interesting
to note thatthe people have not understood
this mathematically really well how exactly
this happens how is it a function of thissimilarity
percentage and how does the clustering combined
although it's common sensical butthe exact
mathematical details of it is not very well
known
