Foldover in bad coordinates

> T:=1:
badcoords:=c->display([
plot([x1a,x2a-c*x1a^2,t=0..T],color=blue,thickness=3),
plot([-x1a,x2a-c*x1a^2,t=0..T],color=blue,thickness=3),
plot([y1,y2-c*y1^2,sw=0..1/2],color=red,thickness=1),
plot([-y1,y2-c*y1^2,sw=0..1/2],color=red,thickness=1),
plot([y1,y2-c*y1^2,sw=1/2..1],color=magenta,thickness=3),
plot([-y1,y2-c*y1^2,sw=1/2..1],color=magenta,thickness=3),
seq(
plot([x1b,x2b-c*x1b^2,t=sw..T],color=green),
sw=[seq((k/100)^.8,k=1..99*T)]),
seq(
plot([-x1b,x2b-c*x1b^2,t=sw..T],color=cyan),
sw=[seq((k/100)^.8,k=1..99*T)])],
scaling=unconstrained,
tickmarks=[0,0],
axes=none):

> badcoords(1/2);

> display([badcoords(1/2),
plot([t,0,t=-1..1],color=black,thickness=1),
plot([0,t,t=-0.2..0.15],color=black,thickness=1)]);

> display([badcoords(1/2),
plot([t,0,t=-1..1],color=black,thickness=1),
plot([0,t,t=-0.08..0.15],color=black,thickness=1),
textplot([-0.4,-0.11,`dx1=u dt`],
font=[TIMES,BOLD,14],align=RIGHT),
textplot([-0.4,-0.14,`dx2=(x1^2-x1 u) dt`],
font=[TIMES,BOLD,14],align=RIGHT)],
title=`Reachable set at time 1`,
titlefont=[TIMES,BOLD,18]);

> badcoords(1/4);

> display([badcoords(1/4),
plot([t,0,t=-1..1],color=black,thickness=1),
plot([0,t,t=-0.05..0.2],color=black,thickness=1)]);

> display([badcoords(1/4),
plot([t,0,t=-1..1],color=black,thickness=1),
plot([0,t,t=-0.05..0.2],color=black,thickness=1),
textplot([-0.85,-0.04,`dx1=u dt`],
font=[TIMES,BOLD,14],align=RIGHT),
textplot([-0.85,-0.07,`dx2=(x1^2-x1 u / 2) dt`],
font=[TIMES,BOLD,14],align=RIGHT)],
title=`Reachable set at time 1`,
titlefont=[TIMES,BOLD,18]);

>

>