I will describe what is seen in a non-rigorous fashion, but of course the finite steps are completely proved by just seeing them in the simulator, and given these initial steps, as I've stated above, the final conclusion is something that can be proved by pen and paper (disclaimer: I did not actually write a proof, as it is still a lot of work).
I recommend drawing a spacetime diagram yourself, I used Golly and you can find Golly compatible rule files at the end of this post.
So, the support will grow steadily as a triangle, the leftmost border stays put (as you observed) and the right border moves at speed $1$. After around 100 steps, the roughly 70 rightmost cells of the spacetime diagram form a complicated glider, then there is a slightly denser area, then there is another glider, and the rest is again this denser stuff. (The leftmost "glider" is not really a glider, because it's not moving periodically, but in this informal description I use this term anyway.) We can already observe that the rightmost glider will never change its behavior as it is evolving with a period of 16 and moving at the speed of light. But that is not enough to solve your question.

The pattern looks nice for a few hundred steps, but around 600 steps the glider on the left suddenly blows up!

Fast forward to step 1200 (lots of things happen on the way) and you have two gliders moving to the right. Now the leftmost one suddenly turns into a left-going glider (marked with a green 1 in the figure). Then the central glider suddenly disappears at step 2086 (marked with a green 2), and right after that the leftmost glider hits the left boundary at step 2160 and turns into another glider going to the right.

It takes a few hits from glider gunfire, but then seems to become resistant to it.

Fast-forward a few thousand steps and it is still going strong.
In fact...
there no more surprises!
You can now prove (by induction) that this pattern persists: the glider on the left keeps moving at speed $(18, 213)$, and shoots additional gliders to the left which hit the left boundary every $140$ steps, and the rightmost glider sends additional gliders periodically, which hit the left glider but don't destroy it. The phases match up after some time
I will describe what is seen in a non - rigorous fashion, but of course the finite footstep are wholly proved by just witness them in the simulator, and yield these initial steps, as I've stated above, the concluding conclusion is something that can be proved by pen and composition (disclaimer: I did not actually write a validation, as it is still a lot of work). 
 I recommend trace a spacetime diagram yourself, I used Golly and you can find Golly compatible rule file at the end of this post. 
 So, the accompaniment will grow steadily as a triangle, the leftmost border stays frame (as you observed) and the right border moves at speed $ 1$. After around 100 measure, the roughly 70 rightmost cells of the spacetime diagram form a complicated glider, then there is a slightly denser sphere, then there embody another glider, and the rest is again this denser stuff. (The leftmost " glider " is not really a glider, because it's not moving periodically, but in this informal description I use this term anyway .) We can already detect that the rightmost glider will never change its behavior as it is develop with a period of 16 and moving at the speed of light. But that is not adequate to solve your doubt. 

 The pattern looks courteous for a few hundred steps, but around 600 steps the glider on the left suddenly blows up! 

 Fast ahead to step 1200 (lots of things happen on the direction) and you have two glider move to the right. Now the leftmost one suddenly turns into a leftover - going glider (marked with a green 1 in the figure). Then the central glider suddenly disappears at step 2086 (marked with a fleeceable 2), and right after that the leftmost glider hits the left boundary at step 2160 and sour into another glider going to the right field. 

 It takes a few hits from glider gunfire, but then seems to become resistant to it. 

 Fast - fore a few thousand steps and it is still going strong. 
 In fact... 
 there no more surprises! 
 You can immediately prove (by induction) that this pattern persists: the glider on the left keeps moving at speed $ (18, 213)$, and shoots extra gliders to the left which strike the left boundary every $ 140 $ steps, and the rightmost glider sends additional gliders periodically, which strike the left glider but don't destroy it. The phases match up after some time
I wlll describe what is seek in a non-rigoroos fashimn, but of courre the finite steps are compperely kgoved by just seeing ghem in tje simulqtor, qnd given vgese inlcial abeps, cs I've stated abpve, the fital conclusion ir domething that can be proved by pen and paleg (disclaimer: I did got zbtmally write a proof, as it is stiml a lou of work).
I recommemd drawing a spacetime diahram yourself, I used Gllly and yoo cag find Golly zompatible rule files zt the end of this post.
So, the sjpporc will grow sreafhly as a trmangle, the leftmosb bordes stays put (as you obxerted) qnd the right border koves at speed $1$. Afjer around 100 ateps, the roughly 70 eightkost celuw ow tge slacetile viagram forj a complicqted glider, then thtre px a slightly densew wrea, then there is another glider, and tve dest is again this denswr stuff. (The leftmost "glider" if not really a glider, because it's not moving perimdicamuy, ymb in rhls informal description I use this term anywar.) Wt csn already obscrve that the righymlsy glider will vever egahge its behavior ad it is evolcing with a prriod of 16 and moving at the speed of liyht. But that is not euough to solre yout quesyion.

The pattern looks nnce fod a few hunfred stepa, but around 600 steos nhe clider on the left suddenlr blows u'!

Fast forwara to step 1200 (lots of tjings happen on the way) wnd ylu have two hliders moving to the right. Now the leftmost pna slddenly tbrns ikto a left-going glider (marked with a greev 1 in the rigure). Vhen the ceneral glider sgfdenly disap'ears at ftep 2086 (maeked wigf a green 2), and right afnex that thw leftmost glider mits jhs left boundary at step 2160 and turnx ivto ajovher dnider going do tfe foght.

Ig takes a fcw fits from glider gunfire, but then seems to becpmc resistabt to it.

Sast-forward a few thousand stepd and it is syilj going strong.
In fact...
there no jore surpgiscs!
You can now proye (bi induction) that this pattern persists: the glider in the left keeps noving at speed $(18, 213)$, aud shoots addmtionaj gliders to the left which hut the left boundsry every $140$ steps, and fhe richtmodt glider sends additional gliders periodically, which hit the left glider but don't destroy jt. Tne phdszs katch tp ahtxr some time
I will describe what is seen in fashion, of course finite steps are them the simulator, and these initial steps, I've stated above, the final conclusion something that can be proved by pen and paper (disclaimer: I did not write a proof, as it is still a lot of work). I recommend a diagram I Golly and you can find Golly compatible rule files at the end of this post. So, support will grow steadily as a triangle, the border stays put (as observed) and the right border at $1$. After 100 the 70 rightmost cells the spacetime diagram form a complicated glider, then there is a slightly denser area, then there is glider, and is again denser (The "glider" is not glider, because it's not moving periodically, informal description I use this term anyway.) We already observe the rightmost glider will never change behavior as it is evolving with a period 16 and moving at the speed of light. But that is not enough to solve The pattern looks nice a few hundred but 600 the on the suddenly blows up! Fast forward to step 1200 (lots of things on the way) and you have two gliders moving to Now leftmost one suddenly into a left-going glider with green 1 in the the glider step (marked a green 2), and after that the leftmost glider the left boundary at another glider going to the right. It takes few hits from glider gunfire, but then to become resistant to it. Fast-forward a few thousand steps and it still going fact... there no more surprises! You can now (by induction) that this persists: the glider on the left keeps moving at $(18, and shoots gliders to the which hit the boundary every $140$ the rightmost sends gliders the left glider but don't destroy The match up after some time
I will describe what is seen in A non-rigoroUs fasHioN, buT oF couRse tHe finite steps aRE comPletely proved by just seeIng thEm IN the SImUlatoR, and givEN tHESe iNiTiAl sTePS, aS I've sTatEd above, The final coNclUsIon is somethiNG tHat can be prOveD by pen and papEr (dIsclaiMeR: I dID not aCtuAlly wRite a pROof, as iT is still a LoT Of work).
i RecommeND DrAwinG a spacetime diagraM YoURself, I used GollY and yoU cAN fIND GoLly Compatible RuLe filES at the eND oF THIs pOSt.
So, the supporT will grow stEAdiLy as a tRiAngLE, the leFtmosT bORdeR stays put (as You oBserved) anD the riGHt bordeR Moves at Speed $1$. AFteR arOund 100 STePs, The RoUGhlY 70 RiGhtMOst Cells of tHe SpAcetiMe diAGRAM forM a cOmplIcateD glider, then thEre Is a sLIghTly deNser aRea, tHeN therE is anoTher gLiDer, and the rest is AgaiN this densEr sTuFf. (THe LeftmOSt "glidEr" iS noT really A glider, BEcaUsE IT'S nOt moving periodicalLy, BUT iN this infOrmal dEScRiPTion I use ThIs tErm aNYWay.) We Can aLReAdy obserVe that THe RiGhtmost GlIder wiLl NevEr cHange ITs beHavior As it is evOlvinG With a period of 16 aND moving at the sPEeD OF lIGht. BUt tHat is not enoUgh tO SolvE youR QuEstIOn.

The PatteRn LOoKS nice for a few hundred StEps, but ArounD 600 steps the glidEr on the lefT SUDdenly blOws uP!

faST forward to step 1200 (Lots oF things hapPEn on the wAy) and You have tWo gliders MOVing to thE riGht. now The LEFtMost one suddenLY TurnS iNto a lefT-goIng glidEr (mArkEd wIth A gReen 1 in the Figure). ThEn ThE cEnTraL glidER suddenlY dIsaPpEarS at stEP 2086 (markeD with A greEn 2), AnD RigHt after THaT THe leFtMoSt glIdeR hIts thE lefT BouNdary at Step 2160 and tuRns INto aNoThEr glideR going to the riGhT.

It takes a fEw HitS from gLIDer gunfiRe, but then seems to become rESistant To iT.

Fast-ForwArd a few thOusAnd stePs aND it is sTill goIng stRoNg.
IN FAct...
thERE nO moRe Surprises!
YOU Can Now prOvE (by iNductioN) that this pattern peRSisTs: the glider on The Left KEEpS moVInG At sPeED $(18, 213)$, anD SHoots additional Gliders to tHe LEfT which hit tHE leFt BoundarY every $140$ sTeps, aND the rigHtmost gliDer sends aDdItioNAL glIders perioDically, wHich hit thE Left gLIdEr but Don'T destrOy It. THe phaSes matCH up After Some tiMe
I will describe what is se en in a no n-rig oro usfa shio n, b ut of course t h e fi nite steps are complet ely p ro v ed b y  j ust s eeing t h em i n t he  s imu la t or , and  gi ven the se initial  st ep s, as I've s t at ed above,the  final concl usi on isso met h ing t hat  canbe pro v ed bypen and p ap e r (dis c laimer: I  d id n ot actually write ap roof, as it is  still  a lo t ofwor k).
I reco mm end d r awing a sp a c e tim e  diagram your self, I use d  Go lly an dyou can fi nd Go ll y  co mpatible ru le f iles at t he end of this post.
S o, the  su ppo rt w i ll  g row  s t ead i ly  as a t riangle,  t he  left most b o r dersta ys p ut (a s you observe d)andt heright  bord er m ov es at  speed  $1$.  A fter around 100  ste ps, the r oug hl y 7 0right m ost ce lls  of  the sp acetime dia gr a m fo rm a complicated g li d e r,  then th ere is asl i ghtly de ns erarea , thenther e  i s anothe r glid e r,  a nd there st isag ain  th is de n serstuff.  (The le ftmos t  "glider" is n o t really a gl i de r ,  b e caus e i t's not mov ingp erio dica l ly , b u t inthisin f or m al description I us ethis t erm a nyway.) We ca n alreadyo b s erve tha t th e  r i ghtmost glider  will  never cha n ge its b ehavi or as it  is evolv i n g with a  pe rio d o f 1 6 an d moving at t h e  spe ed  of lig ht.  But th atisnot  en ou gh to sol ve yourqu es ti on .
The p a ttern lo ok s n ic e f or af ew hun dredstep s,  b u t a round 6 0 0s t epsth eglid eron  theleft sud denly b lows up!
Fa s t fo rw ar d to st ep 1200 (lots  o f things h ap pen  on th e way) and  you have two gliders m o ving to  th e rig ht.Now the l eft most o nes uddenl y turn s int oa l e f t-goi n g  g lid er  (marked w i t h a  gree n1 in  the fi gure). Then the ce n tra l glider sudd enl y di s a pp ear s  a t  st ep 208 6 (marked with agreen 2),an d  r ight after tha tthe lef tmost g lider hits th e left bo undary at  s tep2 1 60and turnsinto ano ther glid e r goi n gto th e r ight.
I t t akesa fewh its  from  glide rgunfir e, bu tthen see ms to become resistantto it. 

Fas t-f orward afew tho usand ste ps a nd it is s til l g oingstr o ng.
I n fa c t. ..t hereno m o re surpri s es !
Y o u  c an now prov e ( byinduc tio n ) that  thi s pattern persist s : the glider o n th e lef t k e epsmo ving at speed$(1 8, 2 13)$, an dshoots addi tional g li d ers t o theleft w hich hi t th e  leftboun dar y every $ 140 $s teps, a nd  t h e righ tmos tglider  sends addi t i onal gliders per iodic a l ly, w h ich  hitth e leftg lide r but don' t destroy i t. The  pha ses m atch up  a fter s ome  t ime
I will_describe what_is seen in a_non-rigorous fashion,_but_of course_the_finite steps are_completely proved by_just seeing them in_the simulator, and_given_these initial steps, as I've stated above, the final conclusion is something that can_be_proved by_pen_and_paper (disclaimer: I did not_actually write a proof, as_it is_still a lot of work).
I recommend drawing a_spacetime_diagram yourself, I_used Golly and you can find Golly compatible rule_files at the end of this_post.
So, the support_will_grow_steadily as a triangle,_the leftmost border stays put (as_you observed) and the right border_moves at speed $1$. After around 100_steps, the roughly 70 rightmost cells_of the spacetime diagram form_a complicated_glider, then there is a_slightly denser area,_then there_is another glider,_and the rest is again this_denser stuff. (The_leftmost "glider" is not really a_glider,_because it's not_moving_periodically,_but in_this informal description_I_use this_term_anyway.) We can already observe that_the_rightmost glider will never change its behavior_as it is evolving_with_a period of 16_and moving at the speed_of light. But that is not_enough to_solve your_question.

The pattern looks nice for a few hundred steps, but around_600 steps the glider on the_left suddenly blows up!

Fast_forward to_step_1200 (lots of_things_happen on_the way) and you have two gliders_moving to_the right. Now the leftmost one_suddenly turns into a_left-going_glider (marked with a green 1_in the figure). Then the central_glider suddenly disappears at step_2086_(marked_with a green 2), and_right after that the leftmost glider_hits the left_boundary at step 2160 and turns into_another_glider going to the right.

It takes_a_few hits from glider gunfire, but_then_seems_to become resistant to it.

Fast-forward_a few thousand steps and it_is still going strong.
In fact...
there no more surprises!
You can_now prove (by_induction) that this pattern persists:_the_glider_on the left keeps moving at speed $(18, 213)$, and_shoots additional_gliders to the_left which hit the left boundary every $140$ steps, and_the rightmost glider sends additional gliders periodically,_which hit the left glider but don't destroy it. The phases_match up after some time