A method of producing a single-stranded nucleic acid, comprising: combining in reaction buffer (a) an initial hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the molecule and a 5' subdomain of the molecule, and (iii) a linkage domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, (b) a second catalytic hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the second hairpin molecule and a 5' subdomain of the second hairpin molecule, and (iii) a loop domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, and wherein the 3' toehold domain of the second hairpin molecule is complementary to the 5' subdomain of the initial hairpin molecule, (c) an initial primer complementary to the 3' toehold domain of the initial hairpin molecule, (d) a polymerase having strand displacement activity, and (e) deoxyribonucleotide triphosphates (dNTPs), thereby forming a reaction mixture; and incubating the reaction mixture under conditions that result in nucleic acid polymerization, strand displacement and annealing, for a time sufficient to produce a single-stranded nucleic acid record that is longer than the initial primer. combining in reaction buffer (a) an initial hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the molecule and a 5' subdomain of the molecule, and (iii) a linkage domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, (b) a second catalytic hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the second hairpin molecule and a 5' subdomain of the second hairpin molecule, and (iii) a loop domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, and wherein the 3' toehold domain of the second hairpin molecule is complementary to the 5' subdomain of the initial hairpin molecule, (c) an initial primer complementary to the 3' toehold domain of the initial hairpin molecule, (d) a polymerase having strand displacement activity, and (e) deoxyribonucleotide triphosphates (dNTPs), thereby forming a reaction mixture; and (a) an initial hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the molecule and a 5' subdomain of the molecule, and (iii) a linkage domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, (b) a second catalytic hairpin molecule comprising (i) an unpaired 3' toehold domain, (ii) a paired stem domain formed by intramolecular nucleotide base pairing between a 3' subdomain of the second hairpin molecule and a 5' subdomain of the second hairpin molecule, and (iii) a loop domain, wherein the paired stem domain comprises a molecule or modification that terminates polymerization, and wherein the 3' toehold domain of the second hairpin molecule is complementary to the 5' subdomain of the initial hairpin molecule, (c) an initial primer complementary to the 3' toehold domain of the initial hairpin molecule, (d) a polymerase having strand displacement activity, and (e) deoxyribonucleotide triphosphates (dNTPs), thereby forming a reaction mixture; and incubating the reaction mixture under conditions that result in nucleic acid polymerization, strand displacement and annealing, for a time sufficient to produce a single-stranded nucleic acid record that is longer than the initial primer.