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' Temperature distribution in a thin, square plate.
' The plate is isolated on both sides, heat can only
' escape along the edges. Heat sources warm up the plate
' in one or more points; these points may be toggled on/off by
' tapping somewhere on the plate.
' The strenght of the heat source can be regulated by the slider.
' The other slider sets the thermal conductivity, which is a material
' property. The temperature distribution is shown in colors and in
' numbers.
' The "outside" temperature along the edges is fixed on 0 degrees.
'
graphics ! graphics clear .8,.8,.8
fill color .8,.8,.8 ! draw color 0,0,0
dim to(13,13),q(12,12),in(12,12)
q_in=75 ! labda=0.1 ! cv=1 ! tmax=300 ! in(4,7)=1 ! in(5,3)=1
for i=1 to 11 ! for j=1 to 11
  to(i,j)=20 ! q(i,j)=20*cv
  next j ! next i
for i=0 to 12
  to(0,i)=0 ! to(12,i)=0 ! to(i,0)=0 ! to(i,12)=0
  next i
for i=0 to 10
  t=i/10 ! t_color(t) ! fill circle 85+60*i,750 size 15
  draw text n2a$(i*tmax/10,3,0) at 55+60*i,770
  next i
draw font size 16
slider "heat" value .5 at 70,820 hsize 630
draw text "heat source" at 330,800
draw text "zero" at 70,800 ! draw text "max" at 670,800
slider "cond" value .5 at 70,880 hsize 630
draw text "thermal conductivity" at 285,860
draw text "zero" at 70,860 ! draw text "max" at 670,860
draw color .3,.3,.3
loop:
disp(to)
for i=1 to 11 ! for j=1 to 11
  q(i,j) += labda*(to(i-1,j)+to(i+1,j)+to(i,j-1)+to(i,j+1)-4*to(i,j))
  q(i,j) += q_in*in(i,j)
  next j ! next i
for i=1 to 11 ! for j=1 to 11 ! to(i,j)=q(i,j)/cv ! next j ! next i
if slider_changed("heat") then q_in=150*slider_value("heat")
if slider_changed("cond") then labda=0.25*slider_value("cond")
get touch 0 as xt,yt
if xt>0 and xt>50 and xt<720 and yt>50 and yt<720 then
  x=floor((xt+10)/60) ! y=floor((yt+10)/60) ! in(x,y)=1-in(x,y)
  end if
goto loop
end

def t_color(t)
if t<0 then t=0 ! if t>1 then t=1
if t<0.2 then
  r=0 ! g=0 ! b=5*t
  else
  if t<0.7 then
    r=2*(t-0.2) ! g=0 ! b=2*(0.7-t)
    else
    if t<0.9 then
      r=1 ! g=5*(t-0.7) ! b=0
      else
      r=1 ! g=1 ! b=10*(t-0.9)
      end if
    end if
  end if
fill color r,g,b
end def

def disp (t(,))
graphics lock
for i=1 to 11 ! for j=1 to 11
  x=50+60*(i-1) ! y=50+60*(j-1)
  t_color(t(i,j)/.tmax)! fill rect x,y to x+60,y+60
  draw text floor(t(i,j)) at x+10,y+20
  next j ! next i
for s=50 to 710 step 60 
  draw line 50,s to 710,s ! draw line s,50 to s,710
  next s
graphics unlock
end def

def n2a$(num,lang,dec)
b$="               "
fac=10^dec
num$=floor(fac*num+.5)/fac
tot=lang-len(num$)
if tot<1 then tot=1
a$=substr$(b$,1,tot) & num$
n2a$=a$
end def