The telautograph is an ancestor of the modern fax machine. It transmits electrical signals representing the position of a pen or tracer at the sending station to repeating mechanisms attached to a pen at the receiving station, thus reproducing at the receiving station a drawing, writing, or signature made by the sender. It was the first such device to transmit drawings to a stationary sheet of paper; previous inventions in Europe had used a constantly moving strip of paper to make such transmissions and the pen could not be lifted between words. Surprisingly, at least from a modern perspective, some early telautographs used digital/pulse-based transmission while later more successful devices reverted to analog signaling.

The telautograph's invention is attributed to the American engineer Elisha Gray, who patented it on July 31, 1888. Gray's patent stated that the telautograph would allow "one to transmit his own handwriting to a distant point over a two-wire circuit." It was the first facsimile machine in which the stylus was controlled by horizontal and vertical bars. The telautograph was first publicly exhibited at the 1893 World's Columbian Exposition held in Chicago.

Gray started experimenting in 1887 with analog transmission of the pen position signals using variable resistances as was done in previous devices, but was dissatisfied with the performance he achieved. He then turned to pulse-based or digital pen position transmission.

Gray's early patents show devices to accomplish the required functions over two line wire circuits with a common ground connection. Pulses were sent over each wire to signal small steps of pen movement. Momentary current interruptions of a baseline direct current signaled pen lifting/lowering and paper feed, and changing polarities were used to encode pen movement direction.

While the patent schema's geometry implies vertical and horizontal coordinates, Gray's first practical system (discussed later) had a different coordinate scheme, based on transmitting two radial distances along approximately diagonal directions from two fixed points. Later systems used in the 20th century transmitted the angle of two crank arm joints in a five bar linkage, comprising two pen motor cranks, two pen linkage bars, and the body of the instrument.

In an 1888 interview in The Manufacturer & Builder (Vol. 24: No. 4: pages 85–86) Gray said:

By my invention you can sit down in your office in Chicago, take a pencil in your hand, write a message to me, and as your pencil moves, a pencil here in my laboratory moves simultaneously, and forms the same letters and words in the same way. What you write in Chicago is instantly reproduced here in fac-simile. You may write in any language, use a code or cipher, no matter, a fac-simile is produced here. If you want to draw a picture it is the same, the picture is reproduced here. The artist of your newspaper can, by this device, telegraph his pictures of a railway wreck or other occurrences just as a reporter telegraphs his description in words.

However these first devices were crude to the point of uselessness. Some of his subsequent refinements changed the encoding scheme. They also mention use of four wires for increased speed and accuracy, but the additional wires were later abandoned. It's clear from the commentary in these and other patents that Gray needed to increase the speed and accuracy of his pulse based system, and in fact he patented a large number of increasingly complicated and refined mechanisms to achieve this.