Continuous strand of filaments having gradient-length characteristic implemented by kinky texture and spiral rotational twist, and manufacturing method therefor

A strand for wigs extending in one direction, the strand comprising:

• 40 to 4,000 filaments of one or more types, 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 spiral waveforms 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 (RD) to a bulk density (BD) of the strand which determines an appearance of the strand and varies based on a self-texture and R, is 1.5 or more to 40 or less,
• wherein each of the filaments forms a plurality of windings having irregular shapes and sizes, wherein when waves formed by the plurality of windings are observed by a scanning electron microscope (SEM), the waves are in irregular waveforms having irregular amplitudes and wavelengths;
• wherein when the total number of the windings is N, a base of a triangle formed by connecting troughs and a peak of an ith winding of each of the filaments is Wi, a height of the triangle of the ith 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(P) each representing a percentage of windings +/−P% or more off from Mw and Mh are respectively defined as IRw(P)=sum(F(Wi), where 1≤i≤N)/N and IRh(P) =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(P), 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(P), 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(P) 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.