For those who wondered how I made the flower tunnel in ASM, here's an example of the radial displacement I used.
'lens mapping with style
'sat this morning and made this
'never thought it would be this easy.
'relsoft 2006
'rel.betterwebber.com
option explicit
const SCR_WIDTH = 320 * 1
const SCR_HEIGHT = 240 * 1
const PI = 3.141593
const XMID = SCR_WIDTH \ 2
const YMID = SCR_HEIGHT \ 2
const radius = 64
cls
screen 14,,2
 Â
  dim wid, hei as integer
  dim hypotsquared, radiussquared, h as integer
  dim sx, sy, x1, y1, yt, xt as integer
  dim px, py as integer
  dim minx, miny as integer
  dim pixel as integer
  dim wtemp, htemp as integer
  dim sphereheight, cleaner as integer
  dim angle as single
  dim frame as single
  sphereheight = (radius shr 1)
  cleaner = sphereheight * 10
  RadiusSquared = Radius * Radius
  wid = Radius shl 1
  hei = Radius shl 1
  dim as single fold_off = 0.02
  dim as single fold_scale = 0.07' * sin(timer / 512.0)
  dim as integer fold_num = 3
  dim as integer min_fold_num = 3
  dim as integer fold_counter = 0
  dim as integer old_scale_sign = 0
  dim as integer x, y
  x = 90
  y = 50
  old_scale_sign = sgn(.5 * sin(timer / 4))
do
  screenset 1, 0
  line(0,0)-(319,239),0,bf
 Â
  frame +=1
  fold_off += 0.2 Â
  fold_scale = .5 * sin(timer / 4)
  if sgn(fold_scale*10) <> old_scale_sign then
    fold_num = (fold_num+1) mod 6
    old_scale_sign = sgn(fold_scale*10)
  end if
FOR yt = -(radius\2) TO hei - 1 + (radius\1)
FOR xt = -(radius\2) TO wid - 1 + (radius\1)
   x1 = (xt - Radius)
   y1 = (yt - Radius)
   HypotSquared = (x1 * x1) + (y1 * y1)
   angle = atan2(y1,x1)
   HypotSquared = (HypotSquared) * (((sin((fold_off+PI) + (fold_num) * angle)) * fold_scale)+1)
   'try this
   'HypotSquared = (HypotSquared) * (((sin((fold_off+PI) + (min_fold_num+fold_num) * angle)) * fold_scale)+1)
   IF HypotSquared < (RadiusSquared - Cleaner) THEN
    H = (Sqr(RadiusSquared - HypotSquared))   Â
    Sx = (SphereHeight - H)
    Sy = (SphereHeight - H)
    Sx = Sx * ((x1 shl 16) \ H)
    Sy = Sy * ((y1 shl 16) \ H)
    py = ((Sy shr 16) + yt +x)
    px = ((Sx shr 16) + xt +y)
    pset(xt+x,yt+y), px xor py
   END IF
NEXT xt
NEXT yt
  screensync
  screencopy
loop until inkey$<>""
