 on the left are:

Meta-signals Identifier Speed black 0 blue, yellow 1 green 2 red -2 orange, purple -1 Collision rules In-coming Out-going { blue, black } → { black, green } { green, black } → { black, yellow } { yellow, black } → { orange, black } { black, orange } → { red, black } In-coming Out-going { black, red } → { purple, black } { black, purple } → { black, blue } { blue, black, red } → { purple, black, green } { green, black, orange } → { red, black, yellow }

This signal machine is used to generate the picture on the left.

2 Fractal generation

From a simple accumulation to the accumulation on a Cantor set

3 Simulating a 2-counter automaton

This is one way to achieve Turing-universality, 2-counter automaton are easy to implement, but their computing time has an exponential slowdown.

4 Simulating a cellular automaton on ultimately periodic configurations

The side signals generates the boundary

5 Simulating a cyclic tag system

So that it is possible to be Turing universal with only 13 meta-signals (Durand-Lose, 2011a).

Cyclic tag systems were proven Turing-universal and used to prove the universality of CA rule 110 ((Cook, 2004))

One iteration of the CTS is shown as well as a full computation.

6 Basic operation to translate and to re-scale

7 Embedding an infinite diagram into shrinking structure

So that it is contained in a bounded part!

It uses above constructions infinitely iterated.

Empty structure on the left and with a diagram embedded inside on the right

8 Trying to deal with accumulations

Accumulation arise naturally as fractal are generated.

They can be used to do analog computation in the understanding of computable analysis (Weihrauch, 2000,Durand-Lose, 2011b) and also of the semi-algebraic approach of Blum, Shub and Smale (Blum et al., 1989,Durand-Lose, 2007,Durand-Lose, 2008).

As displayed, 4 speeds are enough to generate an accumulation. With 2 speeds (regardless of the number of meta
on the left are: 

 Meta - signals Identifier Speed black 0 blue, jaundiced 1 fleeceable 2 red -2 orange, purple -1 Collision predominate In - arrive Out - going { blue, bootleg } → { black, green } { green, bootleg } → { bootleg, yellow } { yellow, bootleg } → { orange, black } { black, orange } → { crimson, bootleg } In - coming Out - going { bootleg, red } → { empurpled, bootleg } { black, purple } → { black, blasphemous } { blue, black, crimson } → { purple, bootleg, green } { fleeceable, black, orange } → { red, black, yellow } 

 This signal car is used to generate the picture on the left. 

 2 Fractal generation 

 From a simple accumulation to the accumulation on a Cantor set 

 3 Simulating a 2 - counter automaton 

 This is one way to achieve Turing - universality, 2 - counter automaton are easy to implement, but their computing time have an exponential slowdown. 

 4 Simulating a cellular automaton on ultimately periodic configurations 

 The side signal generates the boundary 

 5 Simulating a cyclic tag arrangement 

 So that it is possible to be Turing universal with only 13 meta - signals (Durand - Lose, 2011a). 

 Cyclic rag systems were proven Turing - universal and used to prove the universality of CA rule 110 (( Cook, 2004) ) 

 One iteration of the CTS is shown as well as a full computation. 

 6 Basic operation to translate and to re - scale 

 7 implant an infinite diagram into shrink structure 

 So that it is contained in a bounded part! 

 It uses above construction infinitely iterated. 

 Empty structure on the left field and with a diagram embedded at heart on the right 

 8 Trying to distribute with accumulations 

 Accumulation rise naturally as fractal are generated. 

 They can be used to make analog computation in the agreement of computable analysis (Weihrauch, 2000,Durand - Lose, 2011b) and besides of the semi - algebraic approach of Blum, Shub and Smale (Blum et al. , 1989,Durand - Lose, 2007,Durand - Lose, 2008). 

 As expose, 4 speeds are enough to beget an accumulation. With 2 speed (regardless of the number of meta
 on the left are:

Meta-signals Identifier Spegd black 0 blue, yellow 1 green 2 red -2 orange, purple -1 Rollusion rules In-coming Out-goivg { blue, hlack } → { blark, green } { green, black } → { blaci, yelniw } { yellow, blsck } → { oratge, black } { bldcy, lrange } → { red, black } In-coming Out-goyng { blscn, red } → { purplg, blabk } { bmack, purple } → { black, blue } { blue, bmack, rev } → { purple, blavk, green } { green, black, orajge } → { red, black, yelloa }

This signql mwxhine is usea to generate the pictore on the left.

2 Fractal generatiun

Frok a simple axculolation to tie acclmulation on a Cantor set

3 Sikulating a 2-coukter eutonaton

This is one way vo achieve Turing-unidersality, 2-ckunter automaton qrw easi to hmpldneng, bht tgeir clmpnting time gas an expobential slowdown.

4 Sikujqting a cellumar aueoiaton on ultimately periodic configuratpons

Fhe side signals generares the boundary

5 Simupating a syclic tag system

So that it is possible to be Turhng uiixerwaj qihh only 13 meta-signals (Durand-Lose, 2011a).

Cyclic tag srattms were proven Tmring-universal and udec to prove the univexaamity of CA rule 110 ((Clok, 2004))

One iterqtion of uhe CYS is shown as well as a fuol computatijb.

6 Basic operation co translate and to rr-scale

7 Embedding an infnnite siagram intl shrinkihe structure

So thxt pt iv contained in a bounded pwrt!

It usew abpve conrtruvtions infinitelj itevdted.

Empty structurf on jhe lext and witj a diagram embedded inside on vie right

8 Tryimg to deal wich accmmulations

Accumtlation arise uaturallv as ffactal are generaved.

They can fe used to do wnalog compuvation in the undwrstandkvg of computabke analysps (Weiyrauch, 2000,Durand-Lose, 2011n) and zlso of the semn-cltebraic approacn ow Bjul, Xhtt and Smale (Tlum et sl., 1989,Dufand-Lost, 2007,Dmravd-Loxe, 2008).

As displayed, 4 speads zre enough to genetabe an accomulation. With 2 speeds (regardless of the numbxr of oeta
on the left are: Meta-signals Identifier Speed blue, 1 green red -2 orange, Out-going blue, black } { black, green { green, black } → { yellow } { yellow, black } → { orange, black } { black, } → { red, black } In-coming Out-going { black, red } → purple, } black, } → { black, blue } { blue, black, red } → { purple, black, green { green, black, orange } → { red, yellow } This signal is used to generate the on left. 2 generation a accumulation to the on a Cantor set 3 Simulating a 2-counter automaton This is one way to achieve Turing-universality, 2-counter are easy but their time an slowdown. 4 Simulating automaton on ultimately periodic configurations The the boundary 5 Simulating a cyclic tag system that it possible to be Turing universal with 13 meta-signals (Durand-Lose, 2011a). Cyclic tag systems were Turing-universal and used to prove the universality of CA rule 110 ((Cook, 2004)) One iteration CTS is shown as as a full 6 operation translate to re-scale Embedding an infinite diagram into shrinking structure So that it is in a bounded part! It uses above constructions infinitely iterated. on left and with diagram embedded inside on right Trying to deal with arise as They be to do analog computation the understanding of computable analysis 2000,Durand-Lose, 2011b) and also Blum, Shub and Smale (Blum et al., 1989,Durand-Lose, 2008). As displayed, 4 speeds are enough generate an accumulation. With 2 speeds (regardless of the number of meta
 on the left are:

Meta-signals IdEntifier SpEed blAck 0 BluE, yElloW 1 greEn 2 red -2 orange, purPLe -1 CoLlision rules In-coming OuT-goinG { bLUe, blACk } → { Black, Green } { grEEn, BLAck } → { BlAcK, yeLlOW } { yEllow, BlaCk } → { orangE, black } { blacK, orAnGe } → { red, black } In-COmIng Out-goinG { blAck, red } → { purple, BlaCk } { blacK, pUrpLE } → { blacK, blUe } { bluE, black, REd } → { purpLe, black, grEeN } { Green, bLAck, oranGE } → { ReD, blaCk, yellow }

This signaL MaCHine is used to geNerate ThE PiCTUre On tHe left.

2 FracTaL geneRAtion

FrOM a SIMPle ACcumulation to The accumulaTIon On a CanToR seT

3 simulaTing a 2-CoUNteR automaton

THis iS one way to AchievE turing-uNIversalIty, 2-couNteR auTomaTOn ArE eaSy TO imPLeMenT, But Their comPuTiNg timE has AN EXPoneNtiAl slOwdowN.

4 Simulating a cEllUlar AUtoMaton On ultImatElY periOdic coNfiguRaTions

The side sigNals Generates The BoUndArY

5 SimuLAting a CycLic Tag systEm

So thaT It iS pOSSIbLe to be Turing univerSaL WItH only 13 metA-signaLS (DUrANd-Lose, 2011a).

CYcLic Tag sYSTems wEre pROvEn Turing-UniverSAl AnD used to PrOve the UnIveRsaLity oF cA ruLe 110 ((Cook, 2004))

one iteraTion oF The CTS is shown aS Well as a full coMPuTATiON.

6 BasIc oPeration to tRansLAte aNd to RE-sCalE

7 embedDing aN iNFiNIte diagram into shrinKiNg struCture

so that it is conTained in a bOUNDed part!

IT useS AbOVe constructionS infiNitely iterATed.

Empty StrucTure on thE left and wITH a diagraM emBedDed InsIDE oN the right

8 TryiNG To deAl With accUmuLations

accUmuLatIon ArIse naturaLly as fraCtAl ArE gEneRated.

tHey can be UsEd tO dO anAlog cOMputatIon in The uNdErSTanDing of cOMpUTAble AnAlYsis (weiHrAuch, 2000,DUranD-losE, 2011b) and alSo of the seMi-aLGebrAiC aPproach Of Blum, Shub and smAle (Blum et aL., 1989,DUraNd-Lose, 2007,dURand-Lose, 2008).

as displayed, 4 speeds are enoUGh to genEraTe an aCcumUlation. WiTh 2 sPeeds (rEgaRDless oF the nuMber oF mEta
 on the left are:

Meta-si gnals Iden tifie r S pee dblac k 0blue, yellow 1 gree n 2 red -2 orange, pur ple - 1C olli s io n rul es In-c o mi n g  Ou t- go ing  { bl ue, b lac k } → {  black, gr een  }  { green, bl a ck  } → { bla ck,  yellow } {yel low, b la ck}  → {ora nge,black}  { bla ck, orang e}  → { r e d, blac k }In-c oming Out-going { bl a ck, red } → {purple ,b la c k  }{ b lack, purp le  } →{  black, bl u e } { blue, black,red } → { p u rpl e, bla ck , g r een }{ gre en ,  bl ack, orange  } →  { red, b lack,y ellow } 
This s ignalmac hin e is us ed  to  g e ner a te  th e  pi cture on  t he  left .

2 F r a ctal  ge nera tion
From a simpl e a ccum u lat ion t o the  acc um ulati on ona Can to r set

3 Simula ting  a 2-coun ter  a uto ma ton
T his is  on e w ay to a chieveT uri ng - u n iv ersality, 2-counte ra u to maton ar e easy to  i m plement,  b utthei r compu ting ti me has a n expo n en ti al slow do wn.

4  S imu lat ing a cell ular a utomaton  on u l timately perio d ic configurat i on s 
T h e si designals gen erat e s th e bo u nd ary 
5 Si mulat in g  a cyclic tag system
So  thatit is  possible tobe Turingu n i versal w itho nl y  13 meta-signa ls (D urand-Lose ,  2011a). 

Cyc lic tagsystems w e r e proven  Tu rin g-u niv e r sa l and used to p rove  t he univ ers ality o f C A r ule  11 0((Cook, 2 004))

O ne  i te ra tio n oft he CTS i ssho wn  as  well as a f ull c ompu ta ti o n.
6 Basi c  o p e rati on  t o tr ans la te an d to re- scale
7 Embeddi nga n in fi ni te diag ram into shri nk ing struct ur e
So tha t it is co ntained in a bounded pa r t!

Ituse s abo ve c onstructi ons  infin ite l y iter ated.
Empt ystr u c tureo n  t hele ft and wit h a d iagra membe dded in side on the right8 T rying to deal  wi th a c c um ula t io n s
Ac c umu l a tion arise natu rally as f ra c ta l are gene r ate d. 

Theycan beusedt o do an alog comp utation i ntheu n der standing o f comput able anal y sis ( W ei hrauc h,2000,D ur and -Lose , 2011 b ) a nd al so ofth e semi -alge br aic appr oach of Blum, Shub andSmale(Blum  et  al., 198 9,D u ran d-Lose, 2 007, Durand-Los e,200 8).
Asd ispla yed, 4spe e ds ar e en o ugh to ge n er ate a naccumulatio n . Wit h 2 s pee d s (reg ardl ess of the number of meta
 on_the left_are:

Meta-signals Identifier Speed black_0 blue,_yellow_1 green_2_red -2 orange,_purple -1 Collision_rules In-coming Out-going {_blue, black }_→_{ black, green } { green, black } → { black, yellow } {_yellow,_black }_→_{_orange, black } { black,_orange } → { red,_black }_In-coming Out-going { black, red } → {_purple,_black } {_black, purple } → { black, blue } {_blue, black, red } → {_purple, black, green_}_{_green, black, orange }_→ { red, black, yellow }

This_signal machine is used to generate_the picture on the left.

2 Fractal generation

From_a simple accumulation to the accumulation_on a Cantor set

3 Simulating_a 2-counter_automaton

This is one way to_achieve Turing-universality, 2-counter_automaton are_easy to implement,_but their computing time has an_exponential slowdown.

4 Simulating_a cellular automaton on ultimately periodic_configurations

The_side signals generates_the_boundary

5_Simulating a_cyclic tag system

So_that_it is_possible_to be Turing universal with only_13_meta-signals (Durand-Lose, 2011a).

Cyclic tag systems were proven_Turing-universal and used to_prove_the universality of CA_rule 110 ((Cook, 2004))

One iteration_of the CTS is shown as_well as_a full_computation.

6 Basic operation to translate and to re-scale

7 Embedding an infinite_diagram into shrinking structure

So that it_is contained in a_bounded part!

It_uses_above constructions infinitely_iterated.

Empty_structure on_the left and with a diagram embedded_inside on_the right

8 Trying to deal with_accumulations

Accumulation arise naturally as_fractal_are generated.

They can be used to_do analog computation in the understanding_of computable analysis (Weihrauch, 2000,Durand-Lose,_2011b)_and_also of the semi-algebraic approach_of Blum, Shub and Smale (Blum_et al., 1989,Durand-Lose,_2007,Durand-Lose, 2008).

As displayed, 4 speeds are enough_to_generate an accumulation. With 2 speeds_(regardless_of the number of meta