mjhjmtu

I use the following code to draw repetitive lines and place nodes in specific locations for later on drawing circles and connecting them with lines.

Is there a simpler way to do this job, as using foreach command or any other possible simpler method.

documentclassbeamer
beamertemplatenavigationsymbolsempty
usepackagetikz
usepackagepgfplots
begindocument
beginframe[t]
frametitle
hspace -1cm
begintikzpicture[scale=.7, transform shape,linecolor/.style=ultra thick, green!40!black,dotline/.style=thin, black, loosely dotted]
pgfmathsetmacroincrmnt.6

draw [thick,-latex](-.3,0) -- (0,0) -- (5,0);
draw [thick,-latex](0,-.3) -- (0,0) -- (0,8);
draw [thick,-latex](6.,0) -- (7,0) -- (14.4,0);
draw [thick,-latex](8,-.2) -- (8,0) -- (8,8);
draw [linecolor] (0,incrmnt*1) node (yal) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 1/12([shift=(0:8)]yal.center) node (ya) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 1/12;
draw [dotline] (0,incrmnt*1) -- +(0:14cm);

draw [linecolor] (0,incrmnt*2) node (ybl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 2/12([shift=(0:8)]ybl.center) node (yb) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 2/12;
draw [dotline] (0,incrmnt*2) -- +(0:14cm);

draw [linecolor] (0,incrmnt*3) node (ycl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 3/12([shift=(0:8)]ycl.center) node (yc) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 3/12;
draw [dotline] (0,incrmnt*3) -- +(0:14cm);

draw [linecolor] (0,incrmnt*4) node (ydl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 4/12([shift=(0:8)]ydl.center) node (yd) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 4/12;
draw [dotline] (0,incrmnt*4) -- +(0:14cm);

draw [linecolor] (0,incrmnt*5) node (yel) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 5/12([shift=(0:8)]yel.center) node (ye) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 5/12;
draw [dotline] (0,incrmnt*5) -- +(0:14cm);

draw [linecolor] (0,incrmnt*6) node (yfl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 6/12([shift=(0:8)]yfl.center) node (yf) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 6/12;
draw [dotline] (0,incrmnt*6) -- +(0:14cm);

draw [linecolor] (0,incrmnt*7) node (ygl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 7/12([shift=(0:8)]ygl.center) node (yg) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 7/12;
draw [dotline] (0,incrmnt*7) -- +(0:14cm);

draw [linecolor] (0,incrmnt*8) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 8/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 8/12;
draw [dotline] (0,incrmnt*8) -- +(0:14cm);

draw [linecolor] (0,incrmnt*9) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 9/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 9/12;
draw [dotline] (0,incrmnt*9) -- +(0:14cm);

draw [linecolor] (0,incrmnt*10) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 10/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 10/12;
draw [dotline] (0,incrmnt*10) -- +(0:14cm);

draw [linecolor] (0,incrmnt*11) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 11/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 11/12;
draw [dotline] (0,incrmnt*11) -- +(0:14cm);

draw [linecolor] (0,incrmnt*12) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 12/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] 12/12;
draw [dotline] (0,incrmnt*12) -- +(0:14cm);

draw [linecolor] (incrmnt*1,0) node (al) +(90:incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 1 ([shift=(0:8)]al.center) node (a) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 1 ([shift=(90:incrmnt*1)]a.center) node (au) ([shift=(90:incrmnt*1)]au.center) node (auu);

draw [linecolor] (incrmnt*2,0) node (bl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 2 ([shift=(0:8)]bl.center) node (b) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 2 ([shift=(90:incrmnt*1)]b.center) node (bu) ([shift=(90:incrmnt*2)]bu.center) node (buu);

draw [linecolor] (incrmnt*3,0) node (cl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 3 ([shift=(0:8)]cl.center) node (c) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 3 ([shift=(90:incrmnt*3)]c.center) node (cu) ([shift=(90:incrmnt*2)]cu.center) node (cuu);

draw [linecolor] (incrmnt*4,0) node (dl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 4 ([shift=(0:8)]dl.center) node (d) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 4 ([shift=(90:incrmnt*5)]d.center) node (du) ([shift=(90:incrmnt*2)]du.center) node (duu);

draw [linecolor] (incrmnt*5,0) node (el) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 5 ([shift=(0:8)]el.center) node (e) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 5 ([shift=(90:incrmnt*7)]e.center) node (eu) ([shift=(90:incrmnt*2)]eu.center) node (euu);

draw [linecolor] (incrmnt*6,0) node (fl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 6 ([shift=(0:8)]fl.center) node (f) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 6 ([shift=(90:incrmnt*9)]f.center) node (fu) ([shift=(90:incrmnt*2)]fu.center) node (fuu);

draw [linecolor] (incrmnt*7,0) node (gl) +(90:incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 7 ([shift=(0:8)]gl.center) node (g) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 7([shift=(90:incrmnt*11)]g.center) node (gu) ([shift=(90:incrmnt*1)]gu.center) node (guu);
endtikzpicture
endframe
enddocument

This is the rest of the code to produce the following drawing

 draw [ultra thick, blue] (au.center) -- (bu.center) (buu.center) -- (cu.center) (cuu.center) -- (du.center) (duu.center) -- (eu.center) (euu.center) -- (fu.center) (fuu.center) -- (gu.center) (guu.center) --+(0:incrmnt*2) node (inf);
draw [thick, black] (inf.center) +(90:incrmnt*1) --(inf.center|-0,0) node [xshift=0cm, yshift=-.35cm] $infty$;


draw [thick, red, fill=red] (au.center) circle (.1) (buu.center) circle (.1) (cuu.center) circle (.1) (duu.center) circle (.1) (euu.center) circle (.1) (fuu.center) circle (.1) (guu.center) circle (.1);

draw [thick, red, fill=white] (a.center) circle (.14) (bu.center) circle (.14) (cu.center) circle (.14) (du.center) circle (.14) (eu.center) circle (.14) (fu.center) circle (.14) (gu.center) circle (.14);

To use a foreach loop, it is enough to identify the numbers that are modified in parallel in each line. In your code, the first lines can easily be factorized by a loop.

The following ones are more difficult to factor because there is no regularity that can be easily used.

Edit: correction of an omission of factorization

 documentclassbeamer
 beamertemplatenavigationsymbolsempty
 usepackagetikz
 usepackagepgfplots
 begindocument
 beginframe[t]
 frametitle
 hspace -1cm
 begintikzpicture[scale=.7, transform shape,linecolor/.style=ultra thick, green!40!black,dotline/.style=thin, black, loosely dotted]
 pgfmathsetmacroincrmnt.6

 draw [thick,-latex](-.3,0) -- (0,0) -- (5,0);
 draw [thick,-latex](0,-.3) -- (0,0) -- (0,8);
 draw [thick,-latex](6.,0) -- (7,0) -- (14.4,0);
 draw [thick,-latex](8,-.2) -- (8,0) -- (8,8);

% Factoring the first 12 operations `draw`:
 foreach y in 1,...,12
 draw [linecolor] (0,incrmnt*y) node (yhl) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] y/12([shift=(0:8)]yhl.center) node (yh) +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] y/12;
 draw [dotline] (0,incrmnt*y) -- +(0:14cm);
 

 draw [linecolor] (incrmnt*1,0) node (al) +(90:incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 1 ([shift=(0:8)]al.center) node (a) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 1 ([shift=(90:incrmnt*1)]a.center) node (au) ([shift=(90:incrmnt*1)]au.center) node (auu);

 draw [linecolor] (incrmnt*2,0) node (bl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 2 ([shift=(0:8)]bl.center) node (b) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 2 ([shift=(90:incrmnt*1)]b.center) node (bu) ([shift=(90:incrmnt*2)]bu.center) node (buu);

 draw [linecolor] (incrmnt*3,0) node (cl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 3 ([shift=(0:8)]cl.center) node (c) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 3 ([shift=(90:incrmnt*3)]c.center) node (cu) ([shift=(90:incrmnt*2)]cu.center) node (cuu);

 draw [linecolor] (incrmnt*4,0) node (dl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 4 ([shift=(0:8)]dl.center) node (d) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 4 ([shift=(90:incrmnt*5)]d.center) node (du) ([shift=(90:incrmnt*2)]du.center) node (duu);

 draw [linecolor] (incrmnt*5,0) node (el) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 5 ([shift=(0:8)]el.center) node (e) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 5 ([shift=(90:incrmnt*7)]e.center) node (eu) ([shift=(90:incrmnt*2)]eu.center) node (euu);

 draw [linecolor] (incrmnt*6,0) node (fl) +(90:incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 6 ([shift=(0:8)]fl.center) node (f) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 6 ([shift=(90:incrmnt*9)]f.center) node (fu) ([shift=(90:incrmnt*2)]fu.center) node (fuu);

 draw [linecolor] (incrmnt*7,0) node (gl) +(90:incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4] -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 7 ([shift=(0:8)]gl.center) node (g) +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] 7([shift=(90:incrmnt*11)]g.center) node (gu) ([shift=(90:incrmnt*1)]gu.center) node (guu);

 endtikzpicture
 endframe
 enddocument

In this answer I focus on reproducing your output with foreach loops. I do not reproduce your named nodes, which are not used anywhere in your code. One can, of course, produce automatically named nodes, which I can add if they happen to be used.

documentclassbeamer
beamertemplatenavigationsymbolsempty
usepackagetikz
begindocument
beginframe[t]
frametitle
hspace -1cm
begintikzpicture[scale=.7, transform shape,
linecolor/.style=ultra thick, green!40!black,
dotline/.style=thin, black, loosely dotted]
pgfmathsetmacroincrmnt.6

draw [thick,-latex](-.3,0) -- (5,0);
draw [thick,-latex](0,-.3) -- (0,8);
draw [thick,-latex](6.,0) -- (14.4,0);
draw [thick,-latex](8,-.2) -- (8,8);
foreach X in 1,...,12

draw [dotline] (0,X*7cm/12) -- ++ (14,0);
draw [linecolor] (-incrmnt/2,X*7cm/12)node[left]X/12 -- ++ (incrmnt,0)
(8-incrmnt/2,X*7cm/12)node[left]X/12-- ++ (incrmnt,0);

foreach X in 1,...,7

draw[linecolor] (3*X/5,-incrmnt/2) node[below]X -- ++ (0,incrmnt)
(8+3*X/5,-incrmnt/2) node[below]X -- ++ (0,incrmnt);
pgfmathtruncatemacrotstabs(X-4)
ifnumtst=3
draw[linecolor] (3*X/5,0) -- ++ (0,7/12)
node[fill,red,circle,inner sep=2pt];
else
draw[linecolor] (3*X/5,0) -- ++ (0,14/12)
node[fill,red,circle,inner sep=2pt];
fi

endtikzpicture
endframe
enddocument