The best replacement for asymptote is tikz.

The best alternatives to asymptote are rated as following:
★★★★★  tikz
★★★★  hole
★★★  metapost
★★  discontinuity
★  gnuplot
★  removable discontinuity
★  matplotlib
  oblique
  tangent

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Speaking about asymptote, one probably shouldn't forget about exponential.

Other search terms related to asymptote and their ratings are:
★★★★★ exponential
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asymptote
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