A strand susceptible for use in wigs extending in one direction, the strand comprising: 40 to 4,000 filaments of one type or 40 to 4,000 filaments of two types or more having different shrinkages, wherein each of the filaments comprises an amorphous organic polymer, a semi-crystalline organic polymer, or an alloy thereof, wherein an external diameter D of a cross-section of the strand is in a range of 0.2 centimeters (cm) or more to 3.0 cm or less, the strand overall has a spiral waveform caused by spiral rotational twists, wherein when the number of spiral rotational twists per meter is R (unit: number of rotation/m), a product of D and R (D*R) is 180 (unit: cm • number of rotation/m) or less, a ratio of a real density to a bulk density of the strand being 1.5 or more to 40 or less, a thickness of each of the filaments of the strand is in a range of 3.33 tex (30 de) or more to 20 tex (180 de) or less, wherein each of the filaments forms a plurality of windings having irregular shapes and sizes by thermal shrinkage, wherein when waves formed by the plurality of windings are observed by a scanning electron microscope, the waves are in irregular waveforms having irregular amplitudes and wavelengths; characterised in that when the total number of the windings is N, a base of a triangle formed by connecting troughs and a peak of an i th winding of each of the filaments is Wi, a height of the triangle of the i th winding is Hi, an average base of triangles of the windings is Mw = sum(Wi, where 1≤i≤N)/N, and an average height of the triangles of the windings is Mh = sum(Hi, where 1≤i≤N)/N, and when functions IR each representing a percentage of windings +/-P % or more off from Mw and Mh are respectively defined as IRw = sum(F(Wi), where 1≤i≤N)/N and lRh = sum(F(Hi), where 1≤i≤N)/N, the strand has an irregular texture that satisfies the condition of IRw(0.05)≥0.05 or IRh(0.05)≥0.05; wherein, in the definition of the function IRw, when x≥(1+P)*Mw or x≤(1-P)*Mw, F(x) = 1; or otherwise, F(x) = 0; wherein in the definition of the function IRh, when x≥(1+P)*Mh or x≤(1-P)*Mh, F(x) = 1; or otherwise, F(x) = 0; wherein a value of the function IR is obtained from an A sampling section having a total length of 250 cm, wherein the A sampling section is obtained by adding the sums of hypotenuses of the triangles observed in each filament of ten filaments, in which the sum of hypotenuses of the triangles observed in each filament is selected to be 25 cm, wherein each of the ten filaments is randomly sampled at random locations in the strand having a randomly sampled length of 30 cm, wherein the triangles each formed by connecting troughs and a peak of each of the windings in the A sampling section has an average base in a range of 0.25 millimeters (mm) or more to less than 6.5 mm and an average height in a range of 0.25 mm or more to less than 6.5 mm. 40 to 4,000 filaments of one type or 40 to 4,000 filaments of two types or more having different shrinkages, wherein each of the filaments comprises an amorphous organic polymer, a semi-crystalline organic polymer, or an alloy thereof, wherein an external diameter D of a cross-section of the strand is in a range of 0.2 centimeters (cm) or more to 3.0 cm or less, the strand overall has a spiral waveform caused by spiral rotational twists, wherein when the number of spiral rotational twists per meter is R (unit: number of rotation/m), a product of D and R (D*R) is 180 (unit: cm • number of rotation/m) or less, a ratio of a real density to a bulk density of the strand being 1.5 or more to 40 or less, a thickness of each of the filaments of the strand is in a range of 3.33 tex (30 de) or more to 20 tex (180 de) or less, wherein each of the filaments forms a plurality of windings having irregular shapes and sizes by thermal shrinkage, wherein when waves formed by the plurality of windings are observed by a scanning electron microscope, the waves are in irregular waveforms having irregular amplitudes and wavelengths; characterised in that when the total number of the windings is N, a base of a triangle formed by connecting troughs and a peak of an i th winding of each of the filaments is Wi, a height of the triangle of the i th winding is Hi, an average base of triangles of the windings is Mw = sum(Wi, where 1≤i≤N)/N, and an average height of the triangles of the windings is Mh = sum(Hi, where 1≤i≤N)/N, and when functions IR each representing a percentage of windings +/-P % or more off from Mw and Mh are respectively defined as IRw = sum(F(Wi), where 1≤i≤N)/N and lRh = sum(F(Hi), where 1≤i≤N)/N, the strand has an irregular texture that satisfies the condition of IRw(0.05)≥0.05 or IRh(0.05)≥0.05; wherein, in the definition of the function IRw, when x≥(1+P)*Mw or x≤(1-P)*Mw, F(x) = 1; or otherwise, F(x) = 0; wherein in the definition of the function IRh, when x≥(1+P)*Mh or x≤(1-P)*Mh, F(x) = 1; or otherwise, F(x) = 0; wherein a value of the function IR is obtained from an A sampling section having a total length of 250 cm, wherein the A sampling section is obtained by adding the sums of hypotenuses of the triangles observed in each filament of ten filaments, in which the sum of hypotenuses of the triangles observed in each filament is selected to be 25 cm, wherein each of the ten filaments is randomly sampled at random locations in the strand having a randomly sampled length of 30 cm, wherein the triangles each formed by connecting troughs and a peak of each of the windings in the A sampling section has an average base in a range of 0.25 millimeters (mm) or more to less than 6.5 mm and an average height in a range of 0.25 mm or more to less than 6.5 mm.